salim-barzani

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0 years, 221 days

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These are replies submitted by salim-barzani

@nm  i try to explain in this file 


 

restart

with(PDEtools)

with(LinearAlgebra)

with(Physics)

with(SolveTools)

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

(1)

_local(gamma)

Warning, A new binding for the name `gamma` has been created. The global instance of this name is still accessible using the :- prefix, :-`gamma`.  See ?protect for details.

 

declare(Omega(x, t)); declare(U(xi)); declare(u(x, y, z, t)); declare(Q(xi)); declare(V(xi))

Omega(x, t)*`will now be displayed as`*Omega

 

U(xi)*`will now be displayed as`*U

 

u(x, y, z, t)*`will now be displayed as`*u

 

Q(xi)*`will now be displayed as`*Q

 

V(xi)*`will now be displayed as`*V

(2)

pde1 := I*(diff(Omega(x, t)^m, t))+alpha*(diff(Omega(x, t)^m, `$`(x, 2)))+I*beta*(diff(abs(Omega(x, t))^(2*n)*Omega(x, t)^m, x))+m*sigma*Omega(x, t)^m*(diff(W(t), t)) = I*gamma*abs(Omega(x, t))^(2*n)*(diff(Omega(x, t)^m, x))+delta*abs(Omega(x, t))^(4*n)*Omega(x, t)^m

I*Omega(x, t)^m*m*(diff(Omega(x, t), t))/Omega(x, t)+alpha*(Omega(x, t)^m*m^2*(diff(Omega(x, t), x))^2/Omega(x, t)^2+Omega(x, t)^m*m*(diff(diff(Omega(x, t), x), x))/Omega(x, t)-Omega(x, t)^m*m*(diff(Omega(x, t), x))^2/Omega(x, t)^2)+I*beta*(abs(Omega(x, t))^(2*n)*n*((diff(Omega(x, t), x))*conjugate(Omega(x, t))+Omega(x, t)*(diff(conjugate(Omega(x, t)), x)))*Omega(x, t)^m/abs(Omega(x, t))^2+abs(Omega(x, t))^(2*n)*Omega(x, t)^m*m*(diff(Omega(x, t), x))/Omega(x, t))+m*sigma*Omega(x, t)^m*(diff(W(t), t)) = I*gamma*abs(Omega(x, t))^(2*n)*Omega(x, t)^m*m*(diff(Omega(x, t), x))/Omega(x, t)+delta*abs(Omega(x, t))^(4*n)*Omega(x, t)^m

(3)

NULL

ode := 4*V(xi)^4*n^2*sigma+(-4*beta*k*m*n^2+4*gamma*k*m*n^2)*V(xi)^3+(4*alpha*k^2*m^2*n^2-4*delta^2*m*n^2+4*m*n^2*w)*V(xi)^2-2*V(xi)*(diff(diff(V(xi), xi), xi))*alpha*m*n+(-alpha*m^2+2*alpha*m*n)*(diff(V(xi), xi))^2 = 0

4*V(xi)^4*n^2*sigma+(-4*beta*k*m*n^2+4*gamma*k*m*n^2)*V(xi)^3+(4*alpha*k^2*m^2*n^2-4*delta^2*m*n^2+4*m*n^2*w)*V(xi)^2-2*V(xi)*(diff(diff(V(xi), xi), xi))*alpha*m*n+(-alpha*m^2+2*alpha*m*n)*(diff(V(xi), xi))^2 = 0

(4)

L := Omega(x, t) = U(xi)*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau))

Omega(x, t) = U(xi)*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau))

(5)

T := U(xi) = V(xi)^(1/(2*n))

U(xi) = V(xi)^((1/2)/n)

(6)

NULL

ode1 := U(xi)^3*U(xi)^(-1+2*n)*beta*k*m-U(xi)^2*gamma*U(xi)^(2*n)*k*m+U(xi)^2*delta^2*m+I*U(xi)^2*(diff(U(xi), xi))*U(xi)^(-1+2*n)*beta*m-I*U(xi)*(diff(U(xi), xi))*gamma*U(xi)^(2*n)*m-(2*I)*U(xi)*(diff(U(xi), xi))*alpha*k*m^2-U(xi)^2*alpha*k^2*m^2-U(xi)^2*m*w-I*U(xi)*(diff(U(xi), xi))*m*c[0]+(2*I)*U(xi)^2*(diff(U(xi), xi))*U(xi)^(-1+2*n)*beta*n+(diff(U(xi), xi))^2*alpha*m^2-sigma*U(xi)^(4*n)*U(xi)^2+U(xi)*(diff(diff(U(xi), xi), xi))*alpha*m-(diff(U(xi), xi))^2*alpha*m = 0

U(xi)^3*U(xi)^(-1+2*n)*beta*k*m-U(xi)^2*gamma*U(xi)^(2*n)*k*m+U(xi)^2*delta^2*m+I*U(xi)^2*(diff(U(xi), xi))*U(xi)^(-1+2*n)*beta*m-I*U(xi)*(diff(U(xi), xi))*gamma*U(xi)^(2*n)*m-(2*I)*U(xi)*(diff(U(xi), xi))*alpha*k*m^2-U(xi)^2*alpha*k^2*m^2-U(xi)^2*m*w-I*U(xi)*(diff(U(xi), xi))*m*c[0]+(2*I)*U(xi)^2*(diff(U(xi), xi))*U(xi)^(-1+2*n)*beta*n+(diff(U(xi), xi))^2*alpha*m^2-sigma*U(xi)^(4*n)*U(xi)^2+U(xi)*(diff(diff(U(xi), xi), xi))*alpha*m-(diff(U(xi), xi))^2*alpha*m = 0

(7)

S := diff(G(xi), `$`(xi, 2))+(2*m*mu+lambda)*(diff(G(xi), xi))+mu = 0

diff(diff(G(xi), xi), xi)+(2*m*mu+lambda)*(diff(G(xi), xi))+mu = 0

(8)

S1 := dsolve(S, G(xi))

G(xi) = -exp(-(2*m*mu+lambda)*xi)*c__1/(2*m*mu+lambda)-mu*xi/(2*m*mu+lambda)+c__2

(9)

S2 := diff(G(xi) = -exp(-(2*m*mu+lambda)*xi)*c__1/(2*m*mu+lambda)-mu*xi/(2*m*mu+lambda)+c__2, xi)

diff(G(xi), xi) = -(-2*m*mu-lambda)*exp(-(2*m*mu+lambda)*xi)*c__1/(2*m*mu+lambda)-mu/(2*m*mu+lambda)

(10)

K := V(xi) = a[-1]/(m+1/(diff(G(xi), xi)))+a[0]+a[1]*(m+1/(diff(G(xi), xi)))

V(xi) = a[-1]/(m+1/(diff(G(xi), xi)))+a[0]+a[1]*(m+1/(diff(G(xi), xi)))

(11)

case1 := {alpha = alpha, beta = gamma, delta = delta, gamma = gamma, k = k, lambda = 0, m = 2*n, mu = mu, n = n, sigma = 32*alpha*mu^2*n^4/a[-1]^2, w = -2*alpha*k^2*n-4*alpha*mu^2*n+delta^2, a[-1] = a[-1], a[0] = 0, a[1] = 0}

{alpha = alpha, beta = gamma, delta = delta, gamma = gamma, k = k, lambda = 0, m = 2*n, mu = mu, n = n, sigma = 32*alpha*mu^2*n^4/a[-1]^2, w = -2*alpha*k^2*n-4*alpha*mu^2*n+delta^2, a[-1] = a[-1], a[0] = 0, a[1] = 0}

(12)

F1 := subs(case1, K)

V(xi) = a[-1]/(2*n+1/(diff(G(xi), xi)))

(13)

F2 := subs(case1, ode)

128*V(xi)^4*n^6*alpha*mu^2/a[-1]^2+(16*alpha*k^2*n^4-8*delta^2*n^3+8*n^3*(-2*alpha*k^2*n-4*alpha*mu^2*n+delta^2))*V(xi)^2-4*V(xi)*(diff(diff(V(xi), xi), xi))*alpha*n^2 = 0

(14)

``

(15)

W1 := subs(S2, F1)

V(xi) = a[-1]/(2*n+1/(-(-2*m*mu-lambda)*exp(-(2*m*mu+lambda)*xi)*c__1/(2*m*mu+lambda)-mu/(2*m*mu+lambda)))

(16)

W2 := subs(case1, W1)

V(xi) = a[-1]/(2*n+1/(exp(-4*mu*n*xi)*c__1-(1/4)/n))

(17)

odetest(W2, F2)

0

(18)

NULL

NULL

T2 := subs(W2, T)

U(xi) = (a[-1]/(2*n+1/(exp(-4*mu*n*xi)*c__1-(1/4)/n)))^((1/2)/n)

(19)

T3 := subs(T2, L)

Omega(x, t) = (a[-1]/(2*n+1/(exp(-4*mu*n*xi)*c__1-(1/4)/n)))^((1/2)/n)*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau))

(20)

condition1 := c[0] = -2*alpha*k*m; condition2 := beta = gamma*m/(m+2*n)

c[0] = -2*alpha*k*m

 

beta = gamma*m/(m+2*n)

(21)

n := 2; M := 1

2

 

1

(22)

P := subs(case1, ode1)

4*U(xi)^2*delta^2-(32*I)*U(xi)*(diff(U(xi), xi))*alpha*k-16*U(xi)^2*alpha*k^2-4*U(xi)^2*(-4*alpha*k^2-8*alpha*mu^2+delta^2)-(4*I)*U(xi)*(diff(U(xi), xi))*c[0]+(4*I)*U(xi)^5*(diff(U(xi), xi))*gamma+12*(diff(U(xi), xi))^2*alpha-512*alpha*mu^2*U(xi)^10/a[-1]^2+4*U(xi)*(diff(diff(U(xi), xi), xi))*alpha = 0

(23)

P1 := subs(case1, T2)

U(xi) = (a[-1]/(4+1/(exp(-8*mu*xi)*c__1-1/8)))^(1/4)

(24)

Pe := odetest(P1, P)

-(512*I)*mu*c__1*(8*c__1*a[-1]/(exp(8*mu*xi)+8*c__1)-a[-1]*exp(8*mu*xi)/(exp(8*mu*xi)+8*c__1))^(1/2)*exp(16*mu*xi)*alpha*k/((exp(8*mu*xi)-8*c__1)*(exp(8*mu*xi)+8*c__1)^2)-(16*I)*mu*c__1*(8*c__1*a[-1]/(exp(8*mu*xi)+8*c__1)-a[-1]*exp(8*mu*xi)/(exp(8*mu*xi)+8*c__1))^(1/2)*exp(16*mu*xi)*gamma*a[-1]/((exp(8*mu*xi)-8*c__1)*(exp(8*mu*xi)+8*c__1)^2)-(4096*I)*mu*c__1^2*(8*c__1*a[-1]/(exp(8*mu*xi)+8*c__1)-a[-1]*exp(8*mu*xi)/(exp(8*mu*xi)+8*c__1))^(1/2)*exp(8*mu*xi)*alpha*k/((exp(8*mu*xi)-8*c__1)*(exp(8*mu*xi)+8*c__1)^2)+(128*I)*mu*c__1^2*(8*c__1*a[-1]/(exp(8*mu*xi)+8*c__1)-a[-1]*exp(8*mu*xi)/(exp(8*mu*xi)+8*c__1))^(1/2)*exp(8*mu*xi)*gamma*a[-1]/((exp(8*mu*xi)-8*c__1)*(exp(8*mu*xi)+8*c__1)^2)-(64*I)*mu*c__1*(8*c__1*a[-1]/(exp(8*mu*xi)+8*c__1)-a[-1]*exp(8*mu*xi)/(exp(8*mu*xi)+8*c__1))^(1/2)*exp(16*mu*xi)*c[0]/((exp(8*mu*xi)-8*c__1)*(exp(8*mu*xi)+8*c__1)^2)-(512*I)*mu*c__1^2*(8*c__1*a[-1]/(exp(8*mu*xi)+8*c__1)-a[-1]*exp(8*mu*xi)/(exp(8*mu*xi)+8*c__1))^(1/2)*exp(8*mu*xi)*c[0]/((exp(8*mu*xi)-8*c__1)*(exp(8*mu*xi)+8*c__1)^2)

(25)

subs({condition1, condition2}, Pe)

-(512*I)*mu*c__1*(8*c__1*a[-1]/(exp(8*mu*xi)+8*c__1)-a[-1]*exp(8*mu*xi)/(exp(8*mu*xi)+8*c__1))^(1/2)*exp(16*mu*xi)*alpha*k/((exp(8*mu*xi)-8*c__1)*(exp(8*mu*xi)+8*c__1)^2)-(16*I)*mu*c__1*(8*c__1*a[-1]/(exp(8*mu*xi)+8*c__1)-a[-1]*exp(8*mu*xi)/(exp(8*mu*xi)+8*c__1))^(1/2)*exp(16*mu*xi)*gamma*a[-1]/((exp(8*mu*xi)-8*c__1)*(exp(8*mu*xi)+8*c__1)^2)-(4096*I)*mu*c__1^2*(8*c__1*a[-1]/(exp(8*mu*xi)+8*c__1)-a[-1]*exp(8*mu*xi)/(exp(8*mu*xi)+8*c__1))^(1/2)*exp(8*mu*xi)*alpha*k/((exp(8*mu*xi)-8*c__1)*(exp(8*mu*xi)+8*c__1)^2)+(128*I)*mu*c__1^2*(8*c__1*a[-1]/(exp(8*mu*xi)+8*c__1)-a[-1]*exp(8*mu*xi)/(exp(8*mu*xi)+8*c__1))^(1/2)*exp(8*mu*xi)*gamma*a[-1]/((exp(8*mu*xi)-8*c__1)*(exp(8*mu*xi)+8*c__1)^2)+(128*I)*mu*c__1*(8*c__1*a[-1]/(exp(8*mu*xi)+8*c__1)-a[-1]*exp(8*mu*xi)/(exp(8*mu*xi)+8*c__1))^(1/2)*exp(16*mu*xi)*alpha*k*m/((exp(8*mu*xi)-8*c__1)*(exp(8*mu*xi)+8*c__1)^2)+(1024*I)*mu*c__1^2*(8*c__1*a[-1]/(exp(8*mu*xi)+8*c__1)-a[-1]*exp(8*mu*xi)/(exp(8*mu*xi)+8*c__1))^(1/2)*exp(8*mu*xi)*alpha*k*m/((exp(8*mu*xi)-8*c__1)*(exp(8*mu*xi)+8*c__1)^2)

(26)

NULL

NULL

NULL


 

Download explain.mw

@mmcdara  in the code i don't want all parameter maybe 4 or 5 is enough How i do that?

F-P.mw

@acer  last night my work stoped becuase of this physic i will not used anymore untill i something strange appear.

@acer  just some time  a new sign appear with physic they remove , why problem is physic?

@mmcdara is different no one can undrestand except you  best of best thank you so much.

@mmcdara you are legend of the coding

@mmcdara  i look to my old code and find another thing but is not give my answer even 

How you do that is unbliavable , just this is unclear for me why the author just write a[-1],a[1],c[4] 

restart

with(PDEtools)

with(LinearAlgebra)

NULL

with(SolveTools)

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

(1)

lprint

lprint

(2)

declare(Omega(x, t)); declare(U(xi)); declare(u(x, y, z, t)); declare(Q(xi))

Omega(x, t)*`will now be displayed as`*Omega

 

U(xi)*`will now be displayed as`*U

 

u(x, y, z, t)*`will now be displayed as`*u

 

Q(xi)*`will now be displayed as`*Q

(3)

tr := {t = tau, x = (-ZETA*c[3]-tau*c[4]-`Υ`*c[2]+xi)/c[1], y = `Υ`, z = ZETA, u(x, y, z, t) = U(xi)}

pde1 := diff(u(x, y, z, t), `$`(x, 3), z)-4*(diff(u(x, y, z, t), x, t))+4*(diff(u(x, y, z, t), x))*(diff(u(x, y, z, t), x, z))+2*(diff(u(x, y, z, t), `$`(x, 2)))*(diff(u(x, y, z, t), z))+3*(diff(u(x, y, z, t), `$`(y, 2))) = 0

``

L1 := PDEtools:-dchange(tr, pde1, [xi, `Υ`, ZETA, tau, U])

map(int, L1, xi)

ode := %

F := sum(a[i]*(m+1/(diff(G(xi), xi)))^i, i = -1 .. 1)

D1 := diff(F, xi)

S := diff(G(xi), `$`(xi, 2)) = -(2*m*mu+lambda)*(diff(G(xi), xi))-mu

E1 := subs(S, D1)

D2 := diff(E1, xi)

E2 := subs(S, D2)

D3 := diff(E2, xi)

E3 := subs(S, D3)

NULL

NULL

K := U(xi) = F

K1 := diff(U(xi), xi) = E1

K2 := diff(U(xi), `$`(xi, 2)) = E2

K3 := diff(U(xi), `$`(xi, 3)) = E3

NULL

L := eval(ode, {K, K1, K2, K3})

c[1]^3*c[3]*(6*a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^3/((m+1/(diff(G(xi), xi)))^4*(diff(G(xi), xi))^6)-12*a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^3/((m+1/(diff(G(xi), xi)))^3*(diff(G(xi), xi))^5)-6*a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^2*(2*m*mu+lambda)/((m+1/(diff(G(xi), xi)))^3*(diff(G(xi), xi))^4)+6*a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^3/((m+1/(diff(G(xi), xi)))^2*(diff(G(xi), xi))^4)+6*a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^2*(2*m*mu+lambda)/((m+1/(diff(G(xi), xi)))^2*(diff(G(xi), xi))^3)+a[-1]*(2*m*mu+lambda)^2*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/((m+1/(diff(G(xi), xi)))^2*(diff(G(xi), xi))^2)-6*a[1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^3/(diff(G(xi), xi))^4-6*a[1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^2*(2*m*mu+lambda)/(diff(G(xi), xi))^3-a[1]*(2*m*mu+lambda)^2*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/(diff(G(xi), xi))^2)+3*c[2]^2*(a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/((m+1/(diff(G(xi), xi)))^2*(diff(G(xi), xi))^2)-a[1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/(diff(G(xi), xi))^2)-4*c[4]*c[1]*(a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/((m+1/(diff(G(xi), xi)))^2*(diff(G(xi), xi))^2)-a[1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/(diff(G(xi), xi))^2)+3*c[1]^2*c[3]*(a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/((m+1/(diff(G(xi), xi)))^2*(diff(G(xi), xi))^2)-a[1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/(diff(G(xi), xi))^2)^2 = 0

(4)

NULL

# rewritting rule

RR := isolate(m+1/(diff(G(xi), xi))=Phi, diff(G(xi), xi));

diff(G(xi), xi) = 1/(Phi-m)

(5)

# Apply RR and collect wrt Phi

subs(RR, L):
normal(%):
PhiN := collect(numer(lhs(%)), Phi):
PhiD := denom(lhs(%%));

Phi^4

(6)



with(LargeExpressions):

LLE := collect(PhiN, Phi, Veil[phi] ):
LLE / PhiD = 0;

(3*Phi^8*phi[1]+6*Phi^7*phi[2]+Phi^6*phi[3]+Phi^5*phi[4]-Phi^4*phi[5]-Phi^3*phi[6]+Phi^2*phi[7]-6*Phi*phi[8]+3*phi[9])/Phi^4 = 0

(7)

# phi[i] coefficients

CoefficientNullity:=print~( [ seq( phi[i] = simplify(Unveil[phi](phi[i]), size), i=1..LastUsed[phi] ) ] ):

phi[1] = mu^2*a[1]*c[1]^2*c[3]*(2*mu*c[1]+a[1])

 

phi[2] = lambda*mu*a[1]*c[1]^2*c[3]*(2*mu*c[1]+a[1])

 

phi[3] = -8*(mu*c[3]*(m^2*mu^2+m*mu*lambda-(7/8)*lambda^2)*c[1]^3+(3/4)*c[3]*((m^2*a[1]+a[-1])*mu^2+m*mu*lambda*a[1]-(1/2)*lambda^2*a[1])*c[1]^2+(1/2)*mu*c[1]*c[4]-(3/8)*mu*c[2]^2)*a[1]

 

phi[4] = -8*lambda*(c[3]*(m^2*mu^2+m*mu*lambda-(1/8)*lambda^2)*c[1]^3+(3/4)*(m*lambda*a[1]+mu*(m^2*a[1]+2*a[-1]))*c[3]*c[1]^2+(1/2)*c[1]*c[4]-(3/8)*c[2]^2)*a[1]

 

phi[5] = -2*(m^2*mu^2+m*mu*lambda-(1/2)*lambda^2)*((m^2*a[1]+a[-1])*mu+m*lambda*a[1])*c[3]*c[1]^3-3*((m^4*a[1]^2+4*m^2*a[-1]*a[1]+a[-1]^2)*mu^2+2*m*lambda*a[1]*(m^2*a[1]+2*a[-1])*mu+lambda^2*a[1]*(m^2*a[1]-2*a[-1]))*c[3]*c[1]^2-4*c[4]*((m^2*a[1]+a[-1])*mu+m*lambda*a[1])*c[1]+3*c[2]^2*((m^2*a[1]+a[-1])*mu+m*lambda*a[1])

 

phi[6] = -8*a[-1]*(c[3]*(m^2*mu^2+m*mu*lambda-(1/8)*lambda^2)*c[1]^3+(3/2)*(m*lambda*a[1]+mu*(m^2*a[1]+(1/2)*a[-1]))*c[3]*c[1]^2+(1/2)*c[1]*c[4]-(3/8)*c[2]^2)*lambda

 

phi[7] = -8*a[-1]*(mu^2*c[1]^2*c[3]*(mu*c[1]+(3/4)*a[1])*m^4+2*mu*lambda*c[1]^2*c[3]*(mu*c[1]+(3/4)*a[1])*m^3+((1/8)*mu*c[3]*c[1]^3*lambda^2+(3/4)*c[3]*(lambda^2*a[1]+mu^2*a[-1])*c[1]^2+(1/2)*mu*c[1]*c[4]-(3/8)*mu*c[2]^2)*m^2+(3/4)*lambda*(-(7/6)*c[1]^3*c[3]*lambda^2+mu*a[-1]*c[1]^2*c[3]+(2/3)*c[1]*c[4]-(1/2)*c[2]^2)*m-(3/8)*lambda^2*a[-1]*c[1]^2*c[3])

 

phi[8] = a[-1]*lambda*c[3]*(m*mu+lambda)*m*(2*m^2*mu*c[1]+2*lambda*m*c[1]+a[-1])*c[1]^2

 

phi[9] = a[-1]*c[3]*(m*mu+lambda)^2*m^2*(2*m^2*mu*c[1]+2*lambda*m*c[1]+a[-1])*c[1]^2

(8)

COEFFS := solve({phi[1],phi[2],phi[3],phi[4],phi[5],phi[6],phi[7],phi[8],phi[9]}, {a[-1],a[1],mu,c[4]})

(9)

C := solve({phi[1], phi[2], phi[3], phi[4], phi[5], phi[6], phi[7], phi[8], phi[9]}, {a[-1], a[0], a[1], c[4]})

(10)

sols := solve(CoefficientNullity, [a[-1], a[0], a[1], c[4]]); sols := `assuming`([eval(sols)], [b > 0]); whattype(sols); print(cat(`$`('_', 120))); `~`[print](sols)

[[a[-1] = a[-1], a[0] = a[0], a[1] = a[1], c[4] = c[4]]]

 

list

 

________________________________________________________________________________________________________________________

 

[a[-1] = a[-1], a[0] = a[0], a[1] = a[1], c[4] = c[4]]

(11)
 

 

Download mmcdara-new-M-F-P.mw

@janhardo they are unchangable 

@mmcdara I’m not sure why they did that, and I think I’ve deleted all my previous posts about this because of them also hirota operator. That aside, I thought the graph should look like this in 2D—the middle one. 

@mmcdara How i can plot 2D of this data? it will show effect of noise?

@mmcdara 

Thank you so much for providing the code and for your effort! I truly appreciate your help. I have a few questions regarding the implementation:

  1. What happens to the W(t)W(t)W(t) function in the code? You’ve initialized it as w(t)=0w(t) = 0w(t)=0, but is this just the initial condition?

  2. In the line STX := TX_Wfree *~ T_W;, what does this operation mean conceptually?

  3. How can I modify the matrix to include additional data, such as adding a new column?

  4. I’d like to improve the design and visual clarity of the plot directly within the program, without using external tools. I need these plots for my paper and would like to include labels for the axes, specifying whether they represent absolute, real, or imaginary values for each graph. Additionally, is it possible to generate 2D plots for each graph of the STX matrix?

Your assistance is invaluable, and it will significantly enhance my work. I’ll always remember your support and contribution.

 

@nm  i posted the same in mathematica someone at there answered then i read the paper at one place he mention that . and effect of noise he not shown in graph i don't know what is w(t) at his graph 

@nm  when epsilon= +&- 1 the answer satisfy

@nm  thanks for your efort, i did al step as he did in paper i have different method for solving but for skeching graph i must sketch same graph as he did to figure out what is w(t) in him solution function ,in this graph sigma(delta) is zero but in other graph sigma  is not zero and if you watch graph is contain range of x, 
note(W(t)) is brawnian motion) or wiener process, but at all i can't see effect of this function in graph of paper at all


 

restart

with(PDEtools)

with(LinearAlgebra)

with(Physics)

with(SolveTools)

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

(1)

declare(Omega(x, t)); declare(U(xi)); declare(V(xi)); declare(G(xi))

Omega(x, t)*`will now be displayed as`*Omega

 

U(xi)*`will now be displayed as`*U

 

V(xi)*`will now be displayed as`*V

 

G(xi)*`will now be displayed as`*G

(2)

ode := 4*V(xi)^4*n^2*sigma+(-4*beta*k*m*n^2+4*gamma*k*m*n^2)*V(xi)^3+(4*alpha*k^2*m^2*n^2-4*delta^2*m*n^2+4*m*n^2*w)*V(xi)^2-2*V(xi)*(diff(diff(V(xi), xi), xi))*alpha*m*n+(-alpha*m^2+2*alpha*m*n)*(diff(V(xi), xi))^2 = 0

4*V(xi)^4*n^2*sigma+(-4*beta*k*m*n^2+4*gamma*k*m*n^2)*V(xi)^3+(4*alpha*k^2*m^2*n^2-4*delta^2*m*n^2+4*m*n^2*w)*V(xi)^2-2*V(xi)*(diff(diff(V(xi), xi), xi))*alpha*m*n+(-alpha*m^2+2*alpha*m*n)*(diff(V(xi), xi))^2 = 0

(3)

S := (diff(G(xi), xi))^2 = a*G(xi)^2+b*G(xi)^3+c*G(xi)^4

(diff(G(xi), xi))^2 = a*G(xi)^2+b*G(xi)^3+c*G(xi)^4

(4)

S1 := sum(A[i]*G(xi)^i, i = 0 .. 1)

A[0]+A[1]*G(xi)

(5)

S12 := diff(S1, xi)

A[1]*(diff(G(xi), xi))

(6)

S123 := diff(G(xi), xi) = sqrt(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)

diff(G(xi), xi) = (a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)

(7)

subs(S123, S12)

A[1]*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)

(8)

S11 := %

A[1]*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)

(9)

S2 := diff(S11, xi)

(1/2)*A[1]*(2*a*G(xi)*(diff(G(xi), xi))+3*b*G(xi)^2*(diff(G(xi), xi))+4*c*G(xi)^3*(diff(G(xi), xi)))/(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)

(10)

S22 := subs(S123, S2)

(1/2)*A[1]*(2*a*G(xi)*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)+3*b*G(xi)^2*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)+4*c*G(xi)^3*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2))/(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)

(11)

K := V(xi) = S1

V(xi) = A[0]+A[1]*G(xi)

(12)

K1 := diff(V(xi), xi) = S11

diff(V(xi), xi) = A[1]*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)

(13)

K2 := diff(V(xi), xi, xi) = S22

diff(diff(V(xi), xi), xi) = (1/2)*A[1]*(2*a*G(xi)*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)+3*b*G(xi)^2*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)+4*c*G(xi)^3*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2))/(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)

(14)

F := eval(ode, {K, K1, K2})

4*(A[0]+A[1]*G(xi))^4*n^2*sigma+(-4*beta*k*m*n^2+4*gamma*k*m*n^2)*(A[0]+A[1]*G(xi))^3+(4*alpha*k^2*m^2*n^2-4*delta^2*m*n^2+4*m*n^2*w)*(A[0]+A[1]*G(xi))^2-(A[0]+A[1]*G(xi))*A[1]*(2*a*G(xi)*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)+3*b*G(xi)^2*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)+4*c*G(xi)^3*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2))*alpha*m*n/(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)+(-alpha*m^2+2*alpha*m*n)*A[1]^2*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4) = 0

(15)

numer(lhs(4*(A[0]+A[1]*G(xi))^4*n^2*sigma+(-4*beta*k*m*n^2+4*gamma*k*m*n^2)*(A[0]+A[1]*G(xi))^3+(4*alpha*k^2*m^2*n^2-4*delta^2*m*n^2+4*m*n^2*w)*(A[0]+A[1]*G(xi))^2-(A[0]+A[1]*G(xi))*A[1]*(2*a*G(xi)*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)+3*b*G(xi)^2*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)+4*c*G(xi)^3*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2))*alpha*m*n/(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)+(-alpha*m^2+2*alpha*m*n)*A[1]^2*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4) = 0))*denom(rhs(4*(A[0]+A[1]*G(xi))^4*n^2*sigma+(-4*beta*k*m*n^2+4*gamma*k*m*n^2)*(A[0]+A[1]*G(xi))^3+(4*alpha*k^2*m^2*n^2-4*delta^2*m*n^2+4*m*n^2*w)*(A[0]+A[1]*G(xi))^2-(A[0]+A[1]*G(xi))*A[1]*(2*a*G(xi)*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)+3*b*G(xi)^2*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)+4*c*G(xi)^3*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2))*alpha*m*n/(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)+(-alpha*m^2+2*alpha*m*n)*A[1]^2*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4) = 0)) = numer(rhs(4*(A[0]+A[1]*G(xi))^4*n^2*sigma+(-4*beta*k*m*n^2+4*gamma*k*m*n^2)*(A[0]+A[1]*G(xi))^3+(4*alpha*k^2*m^2*n^2-4*delta^2*m*n^2+4*m*n^2*w)*(A[0]+A[1]*G(xi))^2-(A[0]+A[1]*G(xi))*A[1]*(2*a*G(xi)*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)+3*b*G(xi)^2*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)+4*c*G(xi)^3*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2))*alpha*m*n/(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)+(-alpha*m^2+2*alpha*m*n)*A[1]^2*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4) = 0))*denom(lhs(4*(A[0]+A[1]*G(xi))^4*n^2*sigma+(-4*beta*k*m*n^2+4*gamma*k*m*n^2)*(A[0]+A[1]*G(xi))^3+(4*alpha*k^2*m^2*n^2-4*delta^2*m*n^2+4*m*n^2*w)*(A[0]+A[1]*G(xi))^2-(A[0]+A[1]*G(xi))*A[1]*(2*a*G(xi)*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)+3*b*G(xi)^2*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)+4*c*G(xi)^3*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2))*alpha*m*n/(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)+(-alpha*m^2+2*alpha*m*n)*A[1]^2*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4) = 0))

-(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)*(4*delta^2*m*n^2*A[0]^2-4*m*n^2*w*A[0]^2-4*G(xi)^4*n^2*sigma*A[1]^4-8*G(xi)*alpha*k^2*m^2*n^2*A[0]*A[1]+4*G(xi)^3*alpha*c*m*n*A[0]*A[1]-12*G(xi)*gamma*k*m*n^2*A[0]^2*A[1]+12*G(xi)*beta*k*m*n^2*A[0]^2*A[1]+3*G(xi)^2*alpha*b*m*n*A[0]*A[1]+2*G(xi)*a*alpha*m*n*A[0]*A[1]-12*G(xi)^2*gamma*k*m*n^2*A[0]*A[1]^2+12*G(xi)^2*beta*k*m*n^2*A[0]*A[1]^2-4*alpha*k^2*m^2*n^2*A[0]^2+4*beta*k*m*n^2*A[0]^3+G(xi)^4*alpha*c*m^2*A[1]^2-16*G(xi)^3*n^2*sigma*A[0]*A[1]^3+G(xi)^3*alpha*b*m^2*A[1]^2+4*G(xi)^2*delta^2*m*n^2*A[1]^2-24*G(xi)^2*n^2*sigma*A[0]^2*A[1]^2+G(xi)^2*a*alpha*m^2*A[1]^2-4*G(xi)^2*m*n^2*w*A[1]^2-16*G(xi)*n^2*sigma*A[0]^3*A[1]-4*gamma*k*m*n^2*A[0]^3-4*n^2*sigma*A[0]^4-4*G(xi)^3*gamma*k*m*n^2*A[1]^3+4*G(xi)^3*beta*k*m*n^2*A[1]^3-4*G(xi)^2*alpha*k^2*m^2*n^2*A[1]^2+2*G(xi)^4*alpha*c*m*n*A[1]^2+G(xi)^3*alpha*b*m*n*A[1]^2+8*G(xi)*delta^2*m*n^2*A[0]*A[1]-8*G(xi)*m*n^2*w*A[0]*A[1]) = 0

(16)

%/(-sqrt(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4))

4*delta^2*m*n^2*A[0]^2-4*m*n^2*w*A[0]^2-4*G(xi)^4*n^2*sigma*A[1]^4-8*G(xi)*alpha*k^2*m^2*n^2*A[0]*A[1]+4*G(xi)^3*alpha*c*m*n*A[0]*A[1]-12*G(xi)*gamma*k*m*n^2*A[0]^2*A[1]+12*G(xi)*beta*k*m*n^2*A[0]^2*A[1]+3*G(xi)^2*alpha*b*m*n*A[0]*A[1]+2*G(xi)*a*alpha*m*n*A[0]*A[1]-12*G(xi)^2*gamma*k*m*n^2*A[0]*A[1]^2+12*G(xi)^2*beta*k*m*n^2*A[0]*A[1]^2-4*alpha*k^2*m^2*n^2*A[0]^2+4*beta*k*m*n^2*A[0]^3+G(xi)^4*alpha*c*m^2*A[1]^2-16*G(xi)^3*n^2*sigma*A[0]*A[1]^3+G(xi)^3*alpha*b*m^2*A[1]^2+4*G(xi)^2*delta^2*m*n^2*A[1]^2-24*G(xi)^2*n^2*sigma*A[0]^2*A[1]^2+G(xi)^2*a*alpha*m^2*A[1]^2-4*G(xi)^2*m*n^2*w*A[1]^2-16*G(xi)*n^2*sigma*A[0]^3*A[1]-4*gamma*k*m*n^2*A[0]^3-4*n^2*sigma*A[0]^4-4*G(xi)^3*gamma*k*m*n^2*A[1]^3+4*G(xi)^3*beta*k*m*n^2*A[1]^3-4*G(xi)^2*alpha*k^2*m^2*n^2*A[1]^2+2*G(xi)^4*alpha*c*m*n*A[1]^2+G(xi)^3*alpha*b*m*n*A[1]^2+8*G(xi)*delta^2*m*n^2*A[0]*A[1]-8*G(xi)*m*n^2*w*A[0]*A[1] = 0

(17)

collect(%, G)

(-4*n^2*sigma*A[1]^4+alpha*c*m^2*A[1]^2+2*alpha*c*m*n*A[1]^2)*G(xi)^4+(4*beta*k*m*n^2*A[1]^3-4*gamma*k*m*n^2*A[1]^3-16*n^2*sigma*A[0]*A[1]^3+alpha*b*m^2*A[1]^2+alpha*b*m*n*A[1]^2+4*alpha*c*m*n*A[0]*A[1])*G(xi)^3+(-4*alpha*k^2*m^2*n^2*A[1]^2+12*beta*k*m*n^2*A[0]*A[1]^2-12*gamma*k*m*n^2*A[0]*A[1]^2+4*delta^2*m*n^2*A[1]^2-24*n^2*sigma*A[0]^2*A[1]^2+a*alpha*m^2*A[1]^2+3*alpha*b*m*n*A[0]*A[1]-4*m*n^2*w*A[1]^2)*G(xi)^2+(-8*alpha*k^2*m^2*n^2*A[0]*A[1]+12*beta*k*m*n^2*A[0]^2*A[1]-12*gamma*k*m*n^2*A[0]^2*A[1]+8*delta^2*m*n^2*A[0]*A[1]-16*n^2*sigma*A[0]^3*A[1]+2*a*alpha*m*n*A[0]*A[1]-8*m*n^2*w*A[0]*A[1])*G(xi)-4*alpha*k^2*m^2*n^2*A[0]^2+4*beta*k*m*n^2*A[0]^3-4*gamma*k*m*n^2*A[0]^3+4*delta^2*m*n^2*A[0]^2-4*n^2*sigma*A[0]^4-4*m*n^2*w*A[0]^2 = 0

(18)

eq0 := -4*alpha*k^2*m^2*n^2*A[0]^2+4*beta*k*m*n^2*A[0]^3-4*gamma*k*m*n^2*A[0]^3+4*delta^2*m*n^2*A[0]^2-4*n^2*sigma*A[0]^4-4*m*n^2*w*A[0]^2 = 0

eq1 := -8*alpha*k^2*m^2*n^2*A[0]*A[1]+12*beta*k*m*n^2*A[0]^2*A[1]-12*gamma*k*m*n^2*A[0]^2*A[1]+8*delta^2*m*n^2*A[0]*A[1]-16*n^2*sigma*A[0]^3*A[1]+2*a*alpha*m*n*A[0]*A[1]-8*m*n^2*w*A[0]*A[1] = 0

eq2 := -4*alpha*k^2*m^2*n^2*A[1]^2+12*beta*k*m*n^2*A[0]*A[1]^2-12*gamma*k*m*n^2*A[0]*A[1]^2+4*delta^2*m*n^2*A[1]^2-24*n^2*sigma*A[0]^2*A[1]^2+a*alpha*m^2*A[1]^2+3*alpha*b*m*n*A[0]*A[1]-4*m*n^2*w*A[1]^2 = 0

eq3 := 4*beta*k*m*n^2*A[1]^3-4*gamma*k*m*n^2*A[1]^3-16*n^2*sigma*A[0]*A[1]^3+alpha*b*m^2*A[1]^2+alpha*b*m*n*A[1]^2+4*alpha*c*m*n*A[0]*A[1] = 0

eq4 := -4*n^2*sigma*A[1]^4+alpha*c*m^2*A[1]^2+2*alpha*c*m*n*A[1]^2 = 0

C := solve({eq0, eq1, eq2, eq3, eq4}, {a, b, c, A[0]})

{a = 4*n^2*(alpha*k^2*m-delta^2+w)/(m*alpha), b = 4*(gamma-beta)*k*n^2*A[1]/((m+n)*alpha), c = 4*n^2*sigma*A[1]^2/(alpha*m*(m+2*n)), A[0] = 0}

(19)

W := q(x, t) = V(xi)^(1/(2*n))

q(x, t) = V(xi)^((1/2)/n)

(20)

S123 := diff(G(xi), xi) = sqrt(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)

diff(G(xi), xi) = (a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)

(21)

dsolve(S, G(xi))

G(xi) = (1/2)*(-b+(-4*a*c+b^2)^(1/2))/c, G(xi) = -(1/2)*(b+(-4*a*c+b^2)^(1/2))/c, G(xi) = -4*a*exp(c__1*a^(1/2))/(exp(xi*a^(1/2))*(4*a*c-b^2+2*exp(c__1*a^(1/2))*b/exp(xi*a^(1/2))-(exp(c__1*a^(1/2)))^2/(exp(xi*a^(1/2)))^2)), G(xi) = -4*a*exp(xi*a^(1/2))/(exp(c__1*a^(1/2))*(4*a*c-b^2+2*exp(xi*a^(1/2))*b/exp(c__1*a^(1/2))-(exp(xi*a^(1/2)))^2/(exp(c__1*a^(1/2)))^2))

(22)

Download AUX-M.mw

is nonsense iam stuck for something like that

@nm  can we have same solution becuase he use case in that paper i need to get the same solution becuase there is function which i must figure out the same solution and i am stuck at this point how he get this two solution, How by assuming he get thus solution i try to use mathematica  but all my code are maple  and i can't get it in there too, and also someone in mathematica check that the solution of paper is not solution and is not satisfy equation 

How i can get the same at lease get the same as mathmatica 

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