Particular solutions of the wave equation with cubic nonlinearity in the class of elliptic functions (Q1118103)

We construct sharp particular solutions of the wave equation \(\square u=\lambda F(u)\) with cubic nonlinearity \(F(u)=u^ 3\), where \(\square\) is the d'Alembert operator in Minkowski space \({\mathbb{R}}^{1,3}\), \(\lambda\) is an arbitrary parameter. This equation is used widely in mathematical physics.