Encyclopedia of Complexity and Systems Science

Living Edition
| Editors: Robert A. Meyers

Analytical Soliton Solutions for Some Nonlinear Dynamical Water Waves Models

  • Dianchen Lu
  • Aly R. SeadawyEmail author
  • Asghar Ali
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27737-5_737-1
  • 37 Downloads

Introduction

In different areas of applied science, the investigation of exact travelling wave solutions has played a vital role for describing the character wave problems. For plentiful demonstration of dilemmas in mathematical physics, different nonlinear wave systems have been discussed such as the phenomena flow of heat, plasma physics, and optical fibers. Peripheral of solitary wave is growing daily, so essential to find for exact traveling wave solutions to NLEEs. Exact solutions assist us understand the necessary back ground of problems.

The exact solutions of nonlinear partial differential equations have been investigated by many authors [1–36]. The research of traveling wave solutions of some nonlinear evolution equations derived from such fields played an imperative role in the analysis of some phenomena such as the Bernoulli’s sub-ODE method (Wang et al. 2007), Exp(-Φ(ξ))-expansion method (Islam et al. 2015), extended simple equation method (Ali et al. 2017; Lu et al. 2017a,...

Keywords

Modified Liouville equation The Symmetric Regularized Long Wave (SRLW) equation Fourth-order nonlinear Ablowitz-Kaup-Newell-Segur water wave (AKNS) equation Riccati equation Modified F-Expansion method Soliton solutions 
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© Springer Science+Business Media LLC 2019

Authors and Affiliations

  1. 1.Faculty of ScienceJiangsu UniversityZhenjiangP. R. China
  2. 2.Mathematics Department, Faculty of ScienceTaibah UniversityAl-Madinah Al-MunawarahSaudi Arabia
  3. 3.Department of MathematicsUniversity of EducationMultan CampusPakistan