2.15.18 Klein Gordon \(u_{xx}+u_{yy}+ u^2=0\)

problem number 127

Added December 27, 2018.

Special case Klein Gordon (nonlinear). Solve for \(u(x,y)\) \[ u_{xx}+u_{yy}+ u^2=0 \]

Mathematica


Failed

Maple


\[u \left (x , y\right ) = -6 \left (c_{1}^{2}+c_{2}^{2}\right ) \WeierstrassP \left (c_{1} x +c_{2} y +2 c_{3}, 0, c_{4}\right )\]

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