Results Relating to Hirota Method and Singularity Analysis on Some Nonlinear Waves Equations

  • Chia Chee Pen
  • Zainal Abdul Aziz
Keywords: Hirota method, singularity analysis, D-operator

Abstract

This article investigates on the connection between singularity analysis and Hirota method i.e. a direct method to obtain the multi-soliton solutions of nonlinear waves equations. This includes equations with single bilinear form and coupled system of bilinear forms, together with the use of Hirota D-operator and various types of transformation. In general, finding the proper substitution to obtain the Hirota bilinear form is not an easy task. Singularity analysis is used to formulate this suitable transformation. This analysis is applied to Korteweg-de Vries (KdV), modified KdV and nonlinear Schröedinger (NLS) equations.

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Author Biographies

Chia Chee Pen

Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor

Zainal Abdul Aziz

Ibnu Sina Institute for Fundamental Science Studies, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor

Published
2019-01-19
How to Cite
Chee Pen, C., & Abdul Aziz, Z. (2019). Results Relating to Hirota Method and Singularity Analysis on Some Nonlinear Waves Equations. Journal of Science and Mathematics Letters, 4(1), 75-83. Retrieved from https://ejournal.upsi.edu.my/index.php/JSML/article/view/359