Construction of Infinite Series Exact Solitary Wave Solution of the KPI Equation via an Auxiliary Equation Method

Abstract

The KPI equation is one of most well-known nonlinear evolution equations, which was first used to described two-dimensional shallow water wavs. Recently, it has found important applications in fluid mechanics, plasma ion acoustic waves, nonlinear optics, and other fields. In the process of studying these topics, it is very important to obtain the exact solutions of the KPI equation. In this paper, a general Riccati equation is treated as an auxiliary equation, which is solved to obtain many new types of solutions through several different function transformations. We solve the KPI equation using this general Riccati equation, and construct ten sets of the infinite series exact solitary wave solution of the KPI equation. The results show that this method is simple and effective for the construction of infinite series solutions of nonlinear evolution models.

Periodic Flows in a Viscous Stratified Fluid in a Homogeneous Gravitational Field

“…The influence of viscosity was initially taken into account only in terms of the exponential attenuation of wave amplitudes [1,21]. It was analyzed in more detail when describing the propagation of gravitational surface [23][24][25][26][27][28][29], internal [30] and acoustic waves [31], considering the boundary layers formed simultaneously with the waves.…”