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Exact solution to an approximate sine-Gordon equation in \((n+1)\)-dimensional space. (English) Zbl 0998.35046

Summary: In this Letter, using the qualitative theory of ordinary differential equations, we give a qualitative analysis to a two-dimensional plane autonomous system which is equivalent to an approximate sine-Gordon equation. Then using the first integral method, exact solutions to the approximate sine-Gordon equation in \((n+1)\)-dimensional space are expressed explicitly.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
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