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`How to calculate u = `((∂)/(&P...

Asked: FZ 30 Product: Maple 2022

January 25 2025

1 9

`How to calculate u = `((&PartialD;)/(&PartialD; t) - (&PartialD;)/(&PartialD; x))^(-1)(z)?

restart;

>	with(PDEtools):

>	alias(z=z(x,y,t), u=u(x,y,t))

(1)

z := 32*delta2^3*(exp((2*a*y*delta2^3 + 2*(x + y + t)^3*(B1 + 2*B2)*delta2^2 + (2*a*delta1^2*y + t)*delta2 + 2*delta1^2*(x + y + t)^3*(B1 + 2*B2))/(delta1^2 + delta2^2)) - exp((-2*a*y*delta2^3 + 4*(B1 + B2/2)*(x + y + t)^3*delta2^2 + (-2*a*delta1^2*y - t)*delta2 + 4*delta1^2*(B1 + B2/2)*(x + y + t)^3)/(delta1^2 + delta2^2)))*a/((delta1^2 + delta2^2)^2*(exp((2*(delta1^2 + delta2^2)*(x + y + t)^3*B2 + 2*delta2*(a*(delta1^2 + delta2^2)*y + t/2))/(delta1^2 + delta2^2)) + exp((2*(delta1^2 + delta2^2)*(x + y + t)^3*B1 - 2*delta2*(a*(delta1^2 + delta2^2)*y + t/2))/(delta1^2 + delta2^2)))^3);

(2)

NULL

Download integ.mw

Simplify equations to get G_x=B.G...

Asked: FZ 30 Product: Maple 2022

December 21 2023

1 0

NULL

prel := {p1 = (1/2)*exp(I*a*x*(1/2)+I*b*t*(1/2))*(I*a*g[1](t, x)+2*(diff(g[1](t, x), x))), p2 = -(1/2)*exp(-I*a*x*(1/2)-I*b*t*(1/2))*(I*a*g[2](t, x)-2*(diff(g[2](t, x), x))), p3 = -(1/2)*exp(-I*a*x*(1/2)-I*b*t*(1/2))*(I*a*g[3](t, x)-2*(diff(g[3](t, x), x)))}

{p1 = (1/2)*exp(((1/2)*I)*a*x+((1/2)*I)*b*t)*(I*a*g[1](t, x)+2*(diff(g[1](t, x), x))), p2 = -(1/2)*exp(-((1/2)*I)*a*x-((1/2)*I)*b*t)*(I*a*g[2](t, x)-2*(diff(g[2](t, x), x))), p3 = -(1/2)*exp(-((1/2)*I)*a*x-((1/2)*I)*b*t)*(I*a*g[3](t, x)-2*(diff(g[3](t, x), x)))}

(1)

Matrix(%id = 36893490201564614396)

(2)

prel1 := {p4 = exp((1/2*I)*a*x+(1/2*I)*b*t)*(-I*lambda*g[1](t, x)+c[1]*g[2](t, x)+c[2]*g[3](t, x)), p5 = exp(-(1/2*I)*a*x-(1/2*I)*b*t)*(I*lambda*g[2](t, x)-c[1]*g[1](t, x)), p6 = exp(-(1/2*I)*a*x-(1/2*I)*b*t)*(I*lambda*g[3](t, x)-c[2]*g[1](t, x))}

{p4 = exp(((1/2)*I)*a*x+((1/2)*I)*b*t)*(-I*lambda*g[1](t, x)+c[1]*g[2](t, x)+c[2]*g[3](t, x)), p5 = exp(-((1/2)*I)*a*x-((1/2)*I)*b*t)*(I*lambda*g[2](t, x)-c[1]*g[1](t, x)), p6 = exp(-((1/2)*I)*a*x-((1/2)*I)*b*t)*(I*lambda*g[3](t, x)-c[2]*g[1](t, x))}