2.15.4 Born Infeld \((1-u_t^2) u_{xx} + 2 u_x u_t u_{xt} - (1+ u_x^2) u_{tt}=0\)

problem number 113

Added December 27, 2018.

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

Born Infeld. Solve for \(u(x,t)\) \[ (1-u_t^2) u_{xx} + 2 u_x u_t u_{xt} - (1+ u_x^2) u_{tt}=0 \]

Mathematica


\[\{\{u(x,t)\to c_1(t+x)+c_2(t-x)\}\}\]

Maple


\[u \left (x , t\right ) = c_{7} \left (\tanh ^{3}\left (c_{1}+c_{2} \left (-t +x \right )\right )\right )+c_{5} \tanh \left (c_{1}+c_{2} \left (-t +x \right )\right )+c_{4}\]

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