An auxiliary ordinary differential equation and the exp-function method | Zendy

Jinliang Zhang | Zendy; Gao Ke-quan | Zendy; Chuang-Feng Chen | Zendy; Jianfang Zhang | Zendy

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An auxiliary ordinary differential equation and the exp-function method

Author(s) -

Jinliang Zhang,

Gao Ke-quan,

Chuang-Feng Chen,

Jianfang Zhang

Publication year - 2011

Publication title -

arab journal of mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.353

H-Index - 11

eISSN - 2588-9214

pISSN - 1319-5166

DOI - 10.1016/j.ajmsc.2011.07.001

Subject(s) - mathematics , exact differential equation , riccati equation , first order partial differential equation , ordinary differential equation , partial differential equation , differential equation , universal differential equation , mathematical analysis , burgers' equation , bernoulli differential equation , korteweg–de vries equation , integro differential equation , function (biology) , nonlinear system , physics , quantum mechanics , evolutionary biology , biology

In this paper, the new idea of finding the exact solutions of the nonlinear evolution equations is introduced. The idea is that the exact solutions of the auxiliary ordinary differential equation are derived by using exp-function method, and then the exact solutions of the nonlinear evolution equations are derived with aid of the auxiliary ordinary differential equation. As examples, the classical KdV equation, Boussinesq equation, (3+1)-dimensional Jimbo–Miwa equation and Benjamin–Bona–Mahony equation are discussed and the exact solutions are derived

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