Ahmed111

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These are questions asked by Ahmed111

Maple continuously shows 'Evaluating' and there is no output. How to fix it?

restart

with(LinearAlgebra)

assume(x::real); assume(t::real); assume(`α__1`::real); assume(`α__2`::real); assume(nu::real)

A2s := Matrix([[H__11*exp(I*v__11)/(`λ__1`-conjugate(`λ__1`))+H__13*exp(I*v__21)/(`λ__1`-conjugate(`λ__2`))+1, H__12*exp(-I*v__11)/(`λ__1`-conjugate(`λ__1`))+H__14*exp(-I*v__21)/(`λ__1`-conjugate(`λ__2`)), H__11*exp(I*v__12)/(`λ__2`-conjugate(`λ__1`))+H__13*exp(I*v__22)/(`λ__2`-conjugate(`λ__2`)), H__12*exp(-I*v__12)/(`λ__2`-conjugate(`λ__1`))+H__14*exp(-I*v__22)/(`λ__2`-conjugate(`λ__2`))], [H__12*exp(I*v__11)/(`λ__1`-conjugate(`λ__1`))+H__14*exp(I*v__21)/(`λ__1`-conjugate(`λ__2`)), 1+H__11*exp(-I*v__11)/(`λ__1`-conjugate(`λ__1`))+H__13*exp(-I*v__21)/(`λ__1`-conjugate(`λ__2`)), H__12*exp(I*v__12)/(`λ__2`-conjugate(`λ__1`))+H__14*exp(I*v__22)/(`λ__2`-conjugate(`λ__2`)), H__11*exp(-I*v__12)/(`λ__2`-conjugate(`λ__1`))+H__13*exp(-I*v__22)/(`λ__2`-conjugate(`λ__2`))], [H__13*exp(I*v__11)/(`λ__1`-conjugate(`λ__1`))+H__33*exp(I*v__21)/(`λ__1`-conjugate(`λ__2`)), H__14*exp(-I*v__11)/(`λ__1`-conjugate(`λ__1`))+H__34*exp(-I*v__21)/(`λ__1`-conjugate(`λ__2`)), 1+H__13*exp(I*v__12)/(`λ__2`-conjugate(`λ__1`))+H__33*exp(I*v__22)/(`λ__2`-conjugate(`λ__2`)), H__14*exp(-I*v__12)/(`λ__2`-conjugate(`λ__1`))+H__34*exp(-I*v__22)/(`λ__2`-conjugate(`λ__2`))], [H__14*exp(I*v__11)/(`λ__1`-conjugate(`λ__1`))+H__34*exp(I*v__21)/(`λ__1`-conjugate(`λ__2`)), H__13*exp(-I*v__11)/(`λ__1`-conjugate(`λ__1`))+H__33*exp(-I*v__21)/(`λ__1`-conjugate(`λ__2`)), H__14*exp(I*v__12)/(`λ__2`-conjugate(`λ__1`))+H__34*exp(I*v__22)/(`λ__2`-conjugate(`λ__2`)), H__13*exp(-I*v__12)/(`λ__2`-conjugate(`λ__1`))+H__33*exp(-I*v__22)/(`λ__2`-conjugate(`λ__2`))+1]])

Matrix(%id = 36893490803012390908)

(1)

vvalue := {v__11 = (conjugate(`λ__1`)-`#msub(mi("λ",fontstyle = "normal"),mn("1"))`)*x+(4*`α__1`*(conjugate(`λ__1`)^3-`λ__1`^3)+2*`α__2`*(conjugate(`λ__1`)^2-`λ__1`^2)-8*nu*(conjugate(`λ__1`)^4-`λ__1`^4))*t, v__12 = (conjugate(`λ__1`)-`#msub(mi("λ",fontstyle = "normal"),mn("2"))`)*x+(4*`α__1`*(conjugate(`λ__1`)^3-`λ__2`^3)+2*`α__2`*(conjugate(`λ__1`)^2-`λ__2`^2)-8*nu*(conjugate(`λ__1`)^4-`λ__2`^4))*t, v__21 = (conjugate(`λ__2`)-`#msub(mi("λ",fontstyle = "normal"),mn("1"))`)*x+(4*`α__1`*(conjugate(`λ__2`)^3-`λ__1`^3)+2*`α__2`*(conjugate(`λ__2`)^2-`λ__1`^2)-8*nu*(conjugate(`λ__2`)^4-`λ__1`^4))*t, v__22 = (conjugate(`λ__2`)-`#msub(mi("λ",fontstyle = "normal"),mn("2"))`)*x+(4*`α__1`*(conjugate(`λ__2`)^3-`λ__2`^3)+2*`α__2`*(conjugate(`λ__2`)^2-`λ__2`^2)-8*nu*(conjugate(`λ__2`)^4-`λ__2`^4))*t}

{v__11 = (conjugate(lambda__1)-`#msub(mi("λ",fontstyle = "normal"),mn("1"))`)*x+(4*alpha__1*(conjugate(lambda__1)^3-lambda__1^3)+2*alpha__2*(conjugate(lambda__1)^2-lambda__1^2)-8*nu*(conjugate(lambda__1)^4-lambda__1^4))*t, v__12 = (conjugate(lambda__1)-`#msub(mi("λ",fontstyle = "normal"),mn("2"))`)*x+(4*alpha__1*(conjugate(lambda__1)^3-lambda__2^3)+2*alpha__2*(conjugate(lambda__1)^2-lambda__2^2)-8*nu*(conjugate(lambda__1)^4-lambda__2^4))*t, v__21 = (conjugate(lambda__2)-`#msub(mi("λ",fontstyle = "normal"),mn("1"))`)*x+(4*alpha__1*(conjugate(lambda__2)^3-lambda__1^3)+2*alpha__2*(conjugate(lambda__2)^2-lambda__1^2)-8*nu*(conjugate(lambda__2)^4-lambda__1^4))*t, v__22 = (conjugate(lambda__2)-`#msub(mi("λ",fontstyle = "normal"),mn("2"))`)*x+(4*alpha__1*(conjugate(lambda__2)^3-lambda__2^3)+2*alpha__2*(conjugate(lambda__2)^2-lambda__2^2)-8*nu*(conjugate(lambda__2)^4-lambda__2^4))*t}

(2)

NULL

A2s2 := Determinant(A2s); dets22 := simplify(A2s2, size); length(%)

8949

(3)

dets22f := simplify(subs(vvalue, dets22))

NULL

Download sol1det.mw

please help, thank you!

restart

with(LinearAlgebra)

alias(u = u(x, t), ub = ub(x, t))

u, ub

(1)

``

z1 := (2*I)*u*(2*gamma*lambda^2+alpha*lambda-1/4)*(diff(ub, x))+(2*I)*ub*(-2*gamma*lambda^2+alpha*lambda-1/4)*(diff(u, x))+I*ub*gamma*(diff(u, x, x, x))+Typesetting[delayDotProduct](4*u*gamma, lambda*ub.u.ub, true)+Typesetting[delayDotProduct](4*ub*gamma, lambda*u.ub.u, true)+Typesetting[delayDotProduct]((3*I)*gamma, ub.u.ub.(diff(u, x)), true)+Typesetting[delayDotProduct]((3*I)*gamma, ub.u.(diff(ub, x)).u, true)+Typesetting[delayDotProduct]((3*I)*gamma, ub.(diff(u, x)).ub.u, true)+Typesetting[delayDotProduct]((3*I)*gamma, (diff(ub, x)).u.ub.u, true)+Typesetting[delayDotProduct](I*gamma, (diff(u, x)).(diff(ub, x, x)), true)-Typesetting[delayDotProduct](I*gamma, (diff(ub, x, x)).(diff(u, x)), true)+Typesetting[delayDotProduct](I*gamma, u.(diff(ub, x, x, x)), true)+Typesetting[delayDotProduct](I*gamma, ub.(diff(u, x, x, x)), true)-Typesetting[delayDotProduct]((2*I)*u*gamma, ub.(3*u.(diff(ub, x))-(4*I)*lambda^3), true)+Typesetting[delayDotProduct]((2*I)*ub*gamma, u.(3*ub.(diff(u, x))-(4*I)*lambda^3), true)+(1/2)*Typesetting[delayDotProduct](-4*gamma*lambda-2*alpha, u.(diff(ub, x, x)), true)+(1/2)*Typesetting[delayDotProduct](4*gamma*lambda+2*alpha, ub.(diff(u, x, x)), true)+(1/2)*Typesetting[delayDotProduct](-4*gamma*lambda-2*alpha, (diff(u, x)).(diff(ub, x)), true)+(1/2)*Typesetting[delayDotProduct](4*gamma*lambda+2*alpha, (diff(ub, x)).(diff(u, x)), true)+(1/2)*Typesetting[delayDotProduct](-(8*I)*gamma*lambda^2-(4*I)*alpha*lambda+I, (diff(ub, x)).u, true)+(1/2)*Typesetting[delayDotProduct](-(8*I)*gamma*lambda^2-(4*I)*alpha*lambda+I, ub.(diff(u, x)), true)-ub*(-2*gamma*lambda+alpha)*(diff(u, x, x))+u*(2*gamma*lambda+alpha)*(diff(ub, x, x))+Typesetting[delayDotProduct](2*u, u.ub.u, true)*alpha-Typesetting[delayDotProduct](2*ub, ub.u.ub, true)*alpha-I*u*gamma*(diff(ub, x, x, x)) = 0

(1/2)*(4*gamma*lambda+2*alpha)*((diff(ub, x)).(diff(u, x)))-ub*(-2*gamma*lambda+alpha)*(diff(diff(u, x), x))+u*(2*gamma*lambda+alpha)*(diff(diff(ub, x), x))+(3*I)*gamma*(`.`(ub, diff(u, x), ub, u))+(3*I)*gamma*(`.`(diff(ub, x), u, ub, u))+I*gamma*((diff(u, x)).(diff(diff(ub, x), x)))+I*gamma*(u.(diff(diff(diff(ub, x), x), x)))+(3*I)*gamma*(`.`(ub, u, ub, diff(u, x)))+(3*I)*gamma*(`.`(ub, u, diff(ub, x), u))+4*ub*gamma*(`.`(lambda*u, ub, u))+4*u*gamma*(`.`(lambda*ub, u, ub))+I*gamma*(ub.(diff(diff(diff(u, x), x), x)))+2*u*(`.`(u, ub, u))*alpha-2*ub*(`.`(ub, u, ub))*alpha-I*gamma*((diff(diff(ub, x), x)).(diff(u, x)))+(1/2)*(-4*gamma*lambda-2*alpha)*((diff(u, x)).(diff(ub, x)))+(1/2)*(4*gamma*lambda+2*alpha)*(ub.(diff(diff(u, x), x)))+(1/2)*(-4*gamma*lambda-2*alpha)*(u.(diff(diff(ub, x), x)))+(1/2)*(-(8*I)*gamma*lambda^2-(4*I)*alpha*lambda+I)*(ub.(diff(u, x)))+(2*I)*u*(2*gamma*lambda^2+alpha*lambda-1/4)*(diff(ub, x))+(2*I)*ub*(-2*gamma*lambda^2+alpha*lambda-1/4)*(diff(u, x))-I*u*gamma*(diff(diff(diff(ub, x), x), x))+(2*I)*ub*gamma*(u.(3*(ub.(diff(u, x)))-(4*I)*lambda^3))+I*ub*gamma*(diff(diff(diff(u, x), x), x))-(2*I)*u*gamma*(ub.(3*(u.(diff(ub, x)))-(4*I)*lambda^3))+(1/2)*(-(8*I)*gamma*lambda^2-(4*I)*alpha*lambda+I)*((diff(ub, x)).u) = 0

(2)

Parse:-ConvertTo1D, "first argument to _Inert_ASSIGN must be assignable"

Error, illegal use of an object as a name

"for m from 0 to 5 do  lambda^m:=coeff(lhs(z1),lambda,m)=0;  od;"

 

NULL

Download compare.mw

What kind of solution is it (see (3))? Why is there no solution when I put the initial condition v(0)=C1? Secondly, eq. (2) can be reduced to a first-order differential equation?

restart

interface(showassumed = 0)

declare(v(y))

(1)

q := v(y)*(diff(diff(diff(v(y), y), y), y))+(2*v(y)-(diff(v(y), y)))*(diff(diff(v(y), y), y))+(diff(v(y), y))*(v(y)^3+v(y)-(diff(v(y), y))) = 0

v(y)*(diff(diff(diff(v(y), y), y), y))+(2*v(y)-(diff(v(y), y)))*(diff(diff(v(y), y), y))+(diff(v(y), y))*(v(y)^3+v(y)-(diff(v(y), y))) = 0

(2)

dsolve(q)

v(y) = ODESolStruc(_a, [{(diff(diff(_b(_a), _a), _a))*_b(_a)^2+_b(_a)*((diff(_b(_a), _a))^2*_a+_a^3-(diff(_b(_a), _a))*_b(_a)+2*(diff(_b(_a), _a))*_a-_b(_a)+_a)/_a = 0}, {_a = v(y), _b(_a) = diff(v(y), y)}, {y = Int(1/_b(_a), _a)+_C1, v(y) = _a}])

(3)

NULL

dsolve({q, v(0) = C1})

v(y) = C1

(4)

NULL

Download CD_ode.mw

I try to find the value of the highest peak by using Optimization. But Maple returns an error with the comment "Error, (in Optimization:-NLPSolve) abs is not differentiable at non-real arguments". How to remove it?

plot.mw

How can we draw the pot function the same as in the attached figure (namely 'pot.png')? The values of V(x) may not be the same.

pot.mw

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