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

Mathematical Sciences - Trang 1-13 - 2022
Dipankar Kumar1, Ahmet Yildirim2, Mohammed K. A. Kaabar3, Hadi Rezazadeh4, Mohammad Esmael Samei5
1Department of Mathematics, Bangabandhu Sheikh Mujibur Rahman Science and Technology University, Gopalganj, Bangladesh
2Department of Mathematics, Faculty of Science, Ege University, Bornova, Turkey
3Institute of Mathematical Sciences, Faculty of Science, Universiti Malaya, Kuala Lumpur, Malaysia
4Faculty of Modern Technologies Engineering, Amol University of Special Modern Technologies, Amol, Iran
5Department of Mathematics, Faculty of Basic Science, Bu-Ali Sina University, Hamedan, Iran

Tóm tắt

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.

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