Madelung representation for complex nonlinear d'Alembert equations in n-dimensional Minkowski space

The Madelung representation $\psi = u\exp(iv)$ is considered for the d'Alembert equation $\square_n\psi - F(|\psi|)\psi = 0$ to develop a technique for finding exact solutions. The authors classify the nonlinear function $F$ for which the amplitude and phase of the d'Alembert equation are related to the solutions of the compatible d'Alembert-Hamiltonian system. The equations are studied in the $n$-dimensional Minkowski space.[A.~Ju.~Obolenskij (Kyïv)]The Madelung representation $\psi = u\exp(iv)$ is considered for the d'Alembert equation $\square_n\psi - F(|\psi|)\psi = 0$ to develop a technique for finding exact solutions. The authors classify the nonlinear function $F$ for which the amplitude and phase of the d'Alembert equation are related to the solutions of the compatible d'Alembert-Hamiltonian system. The equations are studied in the $n$-dimensional Minkowski space.Upprättat; 1995; 20070103 (kani)