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.