2.15.9 Chaffee Infante \(u_t = u_{xx} + \lambda (u^3 - u) = 0\)

problem number 118

Added December 27, 2018.

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

Chaffee Infante equation. Solve for \(u(x,t)\) \[ u_t = u_{xx} + \lambda (u^3 - u) = 0 \]

Mathematica


Failed

Maple


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

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