摘要
To seek new infinite sequence of exact solutions to nonlinear evolution equations, this paper gives the formula of nonlinear superposition of the solutions and Backlund transformation of Riccati equation. Based on tanh-function expansion method and homogenous balance method, new infinite sequence of exact solutions to Zakharov-Kuznetsov equation, Karamotc-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.
To seek new infinite sequence of exact solutions to nonlinear evolution equations, this paper gives the formula of nonlinear superposition of the solutions and Backlund transformation of Riccati equation. Based on tanh-function expansion method and homogenous balance method, new infinite sequence of exact solutions to Zakharov-Kuznetsov equation, Karamotc-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.
基金
Project supported by the National Natural Science Foundation of China(Grant No.10461006)
the Science Research Foundation of Institution of Higher Education of Inner Mongolia Autonomous Region,China(Grant No.NJZZ07031)
the Natural Science Foundation of Inner Mongolia Autonomous Region,China(Grant No.200408020103)
the Natural Science Research Program of Inner Mongolia Normal University,China(Grant No.QN005023)
