2004•Communications in Theoretical PhysicsOpen access

Elliptic Equation and Its Direct Applications to Nonlinear Wave Equations

Zuntao Fu, Zhe Chen, Shida Liu, Liu Shi-Kuo

Abstract

Elliptic equation is taken as an ansatz and applied to solve nonlinear wave equations directly. More kinds of solutions are directly obtained, such as rational solutions, solitary wave solutions, periodic wave solutions and so on. It is shown that this method is more powerful in giving more kinds of solutions, so it can be taken as a generalized method.

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Key concepts: Ansatz, Nonlinear system, Periodic wave, Wave equation, Mathematical analysis, Cnoidal wave, Physics, Mathematics