2.15.17 Klein Gordon \(u_{xx}+u_{yy}+ \lambda u^p=0\)

problem number 126

Added December 27, 2018.

Taken from https://en.wikipedia.org/wiki/List_of_nonlinear_partial_differential_equations

Klein Gordon (nonlinear). Solve for \(u(x,y)\) \[ u_{xx}+u_{yy}+ \lambda u^p=0 \]

Mathematica ✗

ClearAll["Global`*"]; 
pde =  Laplacian[u[x, y], {x, y}] + lambda*u[x, y]^p == 0; 
sol =  AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, y], {x, y}], 60*10]];
 

Failed

Maple ✗

restart; 
pde := diff(u(x,y),x$2)+diff(u(x,y),y$2)+lambda*u(x,y)^p=0; 
cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,u(x,y),'build')),output='realtime'));
 

sol=()

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