2.15.19 Khokhlov Zabolotskaya \(u_{x t} - (u u_x)_x = u_{yy}\)

problem number 128

Added December 27, 2018.

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

Khokhlov Zabolotskaya. Solve for \(u(x,y,t)\) \[ u_{x t} - (u u_x)_x = u_{yy} \]

Mathematica


Failed

Maple


\[u \left (x , y , t\right ) = \frac {c_{1} c_{3}-c_{2}^{2}+\sqrt {c_{1}^{2} c_{3}^{2}-2 c_{1} c_{2}^{2} c_{3}+c_{2}^{4}+2 c_{4} \left (c_{3} t +c_{1} x +c_{2} y +c_{4}\right ) c_{1}^{2}+2 c_{5} c_{1}^{2}}}{c_{1}^{2}}\]

________________________________________________________________________________________