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Question: Simplify equations to get G_x=B.G

Question:Simplify equations to get G_x=B.G

FZ 10 Maple 2022
linearalgebra differential-equations
December 21 2023
2
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NULL
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restart
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with(LinearAlgebra)
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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)
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A := Matrix([[rhs(prel[1]), rhs(prel[2]), rhs(prel[3])]])
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A1 := Transpose(A)

Matrix(%id = 36893490201564614396)

 (2)
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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))}

 (3)
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A2 := Matrix([[rhs(prel1[1]), rhs(prel1[2]), rhs(prel1[3])]]); A3 := Transpose(A2)

Matrix(%id = 36893490201519962460)

 (4)
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NULL

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