2.15.8 Camassa Holm \(u_t + 2 k u_x - u_{xxt} + 3 u u_x = 2 u_x u_{xx}+ u u_{xxx}\)

problem number 117

Added December 27, 2018.

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

Camassa Holm. Solve for \(u(x,t)\) \[ u_t + 2 k u_x - u_{xxt} + 3 u u_x = 2 u_x u_{xx}+ u u_{xxx} \]

Mathematica


Failed

Maple


\[u \left (x , t\right ) = \frac {\RootOf \left (c_{1} c_{5}-c_{1} x +c_{1} \left (\int _{}^{-\frac {-\mathit {\_Z}^{2}+c_{2}}{c_{1}}}\frac {\sqrt {c_{1} \mathit {\_f} +c_{2}}}{\sqrt {-c_{4} c_{1}^{3} \mathit {\_f} +c_{1} \mathit {\_f}^{3}+2 c_{1} \mathit {\_f}^{2} k -c_{1}^{2} c_{2} c_{4}+c_{2} \mathit {\_f}^{2}-c_{3} c_{1}^{2}}}d\mathit {\_f} \right )-c_{2} t -c_{3}\right )^{2}-c_{2}}{c_{1}}\] Answer in terms of RootOf.

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