Functionally invariant solutions of nonlinear Klein–Fock–Gordon equation

摘要

For the first time functionally invariant solutions U(x,y,z,t) of nonlinear Klein–Fock–Gordon equation are obtained. Solutions are found in the form of composite function U=f(W). Function f(W) satisfies to the ordinary nonlinear differential equation of the second order, and W(x,y,z,t) contains arbitrary function F(α). Ansatz α(x,y,z,t) is found from the algebraic equations. The examples for α are given. Proposed approach is illustrated by the solution of sine–Gordon equation.