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

¹ Hefei Thomas School, Hefei, China
² The Second High School Attached to Beijing Normal University International Department, Beijing, China
³ Institute of Plasma Physics, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei, China

American Journal of Computational Mathematics·Volume 12 (2022)·Pages 256–266·Published 9 May 2022·DOI10.4236/ajcm.2022.122016

Abstract

In this paper, we use Riccati equation to construct new solitary wave solu tions 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 p 1 and q 1 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.

KeywordsNonlinear Evolution EquationsHyperbolic FunctionRiccati EquationAuxiliary EquationSolitary Wave Solutions

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

Abstract

References (20)