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Separation transformation and envelope solutions of the higher-dimensional complex nonlinear Klein–Gordon equation. (English) Zbl 1111.81052

Summary: In this paper, the higher-dimensional complex nonlinear Klein–Gordon equation is investigated. We firstly use a transformation to separate this equation into a nonlinear ordinary differential equation (ODE) and a set of partial differential equations (PDE). And then, we solve these two families of equations, respectively. Finally many types of solutions of the higher-dimensional complex nonlinear Klein–Gordon equation are obtained, and when \(N\geqslant 2\), these solutions contain two arbitrary functions which lead to abundant structures.

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
35Q53 KdV equations (Korteweg-de Vries equations)
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