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Clarkson, P.A. and Mansfield, E.L. (1995) Symmetry Reductions and Exact Solutions of Shallow Water Wave Equations. Acta Applicandae Mathematicae, 39, 245-276.
https://doi.org/10.1007/BF00994636

has been cited by the following article:

• TITLE: Using Riccati Equation to Construct New Solitary Solutions of Nonlinear Difference Differential Equations

  AUTHORS: Xinxiang Liu, Kaiwen Cui, Guojiang Wu

  KEYWORDS: Nonlinear Evolution Equations, Hyperbolic Function, Riccati Equation, Auxiliary Equation, Solitary Wave Solutions

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.12 No.2, June 24, 2022

  ABSTRACT: In this paper, we use Riccati equation to construct new solitary wave solutions of the nonlinear evolution equations (NLEEs). Through the new function transformation, the Riccati equation is solved, and many new solitary wave solutions are obtained. Then it is substituted into the (2 + 1)-dimensional BLMP equation and (2 + 1)-dimensional KDV equation as an auxiliary equation. Many types of solitary wave solutions are obtained by choosing different coefficient p1 and q1 in the Riccati equation, and some of them have not been found in other documents. These solutions that we obtained in this paper will be helpful to understand the physics of the NLEEs.