Exact solutions of nonlinear Klein-Fock-Gordon equation

New approach to the integration of nonlinear Klein-Fock-Gordon equation is given. Solutions U(x; y; z; t) are searched in the form of a composite function U = f(W). It is assumed that W(x; y; z; t) simultaneously satisfies to two partial differential equations and f(W) to the self-similar nonlinear...

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Bibliographic Details
Main Authors: Aero, E. L., Bulygin, A. N., Pavlov, Y. V.
Format: Conference Proceeding
Language:English
Subjects:
Equations
Manganese
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Summary:New approach to the integration of nonlinear Klein-Fock-Gordon equation is given. Solutions U(x; y; z; t) are searched in the form of a composite function U = f(W). It is assumed that W(x; y; z; t) simultaneously satisfies to two partial differential equations and f(W) to the self-similar nonlinear ordinary differential equation. Functionally invariant solutions are constructed for W which contain arbitrary function F(α). Ansatz α(x; y; z; t) may be found as a root of linear algebraic equation of variables (x; y; z; t) with coefficients in the form of arbitrary functions of α. Particular expressions of ansatz α are found. Proposed approach is illustrated by the solution of triple sh-Gordon equation.
DOI:10.1109/DD.2012.6402742