10.1007/s40096-022-00501-0

Exploration of some novel solutions to a coupled Schrödinger–KdV equations in the interactions of capillary-gravity waves

  • Dipankar Kumar1,
  • Ahmet Yildirim2,
  • Mohammed K. A. Kaabar*3,
  • Hadi Rezazadeh4,
  • Mohammad Esmael Samei5,
  1. Department of Mathematics, Bangabandhu Sheikh Mujibur Rahman Science and Technology University, Gopalganj, 8100, BD
  2. Department of Mathematics, Faculty of Science, Ege University, Bornova, Izmir, 35100, TR
  3. Institute of Mathematical Sciences, Faculty of Science, Universiti Malaya, Kuala Lumpur, 50603, MY
  4. Faculty of Modern Technologies Engineering, Amol University of Special Modern Technologies, Amol, IR
  5. Department of Mathematics, Faculty of Basic Science, Bu-Ali Sina University, Hamedan, IR

Published in Issue 2022-12-16

How to Cite

Kumar, D., Yildirim, A., Kaabar, M. K. A., Rezazadeh, H., & Samei, M. E. (2022). Exploration of some novel solutions to a coupled Schrödinger–KdV equations in the interactions of capillary-gravity waves. Mathematical Sciences, 18(2 (June 2024). https://doi.org/10.1007/s40096-022-00501-0
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Abstract

Abstract Some novel solutions to a system of coupled Schrödinger–Korteweg–de Vries equations are explored in this work by employing the extended sinh-Gordon equation expansion method to the proposed system. Some novel forms of explicit complex hyperbolic and complex trigonometric function solutions such as singular, combined singular, dark, bright, combined dark–bright, periodic wave, dipole soliton, and other solutions are retrieved and explored into their corresponding system via MAPLE software. Two- and three-dimensional graphs are provided to illustrate this study’s novelty. All combined solutions are particularly new in the interactions of capillary-gravity water waves. Extended sinh-Gordon equation expansion method provides an effective tool to explore new precise wave solutions and overcome the difficulties of the ansatz method. All our results in this work play an essential role in explaining various phenomena in ocean and coastal engineering.

Keywords

  • Soliton solutions,
  • Coupled Schrödinger–KdV equations,
  • Extended sinh-Gordon equation expansion method

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