New application to Riccati equation |
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| Authors: | Taogetusang Sirendaoerji Li Shu-Min |
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| Affiliation: | College of Mathematical Science, Inner Mongolia Normal University, Huhhot 010022, China; College of Mathematical Science, Bao Tou Teachers' College, Bao Tou 014030, China |
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| Abstract: | To seek new infinite sequence of exact solutions to nonlinear evolution equations, this paper gives the formula of nonlinear superposition of the solutions and Bäcklund transformation of Riccati equation. Based on the tanh-function expansion method and homogenous balance method, new infinite sequence of exact solutions to Zakharov–Kuznetsov equation, Karamoto–Sivashinsky equation and the set of (2+1)-dimensional asymmetric Nizhnik–Novikov–Veselov equations are obtained with the aid of symbolic computation system Mathematica. The method is of significance to construct infinite sequence exact solutions to other nonlinear evolution equations. |
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| Keywords: | Riccati equation formula of nonlinear superposition nonlinear evolution equation exact solution |
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