Solitary wave solutions of several nonlinear PDEs modeling shallow water waves

2017/09/15 by Nikolay K. Vitanov, Vitanov, Nikolay K., Tsvetelina Ivanova +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1709.05320

openalex publication_date 2017/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We apply the version of the method of simplest equation called modified method of simplest equation for obtaining exact traveling wave solutions of a class of equations that contain as particular case a nonlinear PDE that models shallow water waves in viscous fluid (Topper-Kawahara equation). As simplest equation we use a version of the Riccati equation. We obtain two exact traveling wave solutions of equations from the studied class of equations and discuss the question of imposing boundary conditions on one of these solutions.

Citations

• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems

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