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Question: How to verify this solution in the given pde.

Question:How to verify this solution in the given pde.

Amna Raja 20 Maple 2016
pde simplification pdetest
April 30 2018
1

restart;
with(DEtools);
assume(r::real, a::real, b::real, upsilon::real, sigma::real, x::real, y::real, t > 0);
assume(sigma > 0); assume(-b^2-r+2 > 0);
V := -2*exp(I*(sqrt(-b^2-r+2)*x+b*y+r*t))*sqrt(1/sigma)*sech(-t*(-2*sqrt(-b^2-r+2)-2*b)-x-y):
pde[1] := I*(diff(V, t))+diff(V, x, x)+diff(V, y, y)+sigma*abs(V^2)*V = 0: evalc(pde[1]);

 

solution.mw
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