A study of resonance Y-type multi-soliton solutions and soliton molecules for new (2+1)-dimensional nonlinear wave equations

Chun-Ku Kuo; Dipankar Kumar; Chieh-Ju Juan; Chun-Ku Kuo; Dipankar Kumar; Chieh-Ju Juan

doi:10.3934/math.20221136

AIMS Mathematics

2022, Volume 7, Issue 12: 20740-20751. doi: 10.3934/math.20221136

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Research article

A study of resonance Y-type multi-soliton solutions and soliton molecules for new (2+1)-dimensional nonlinear wave equations

1.
Department of Aeronautics and Astronautics, Air Force Academy, Kaohsiung 820009, Taiwan
2.
Department of Mathematics, Bangabandhu Sheikh Mujibur Rahman Science and Technology University, Gopalganj 8100, Bangladesh
3.
Department of Aviation Management, Air Force Academy, Kaohsiung 820009, Taiwan

Received: 04 August 2022 Revised: 12 September 2022 Accepted: 19 September 2022 Published: 26 September 2022
MSC : 35C08, 35Q51, 37K40

In this study, a fourth-order nonlinear wave equation with variable coefficients was investigated. Through appropriate choice of the free parameters and using the simplified linear superposition principle (LSP) and velocity resonance (VR), the examined equation can be considered as Hirota–Satsuma–Ito, Calogero–Bogoyavlenskii–Schiff and Jimbo–Miwa equations. The main objective of this study was to obtain novel resonant multi-soliton solutions and investigate inelastic interactions of traveling waves for the above-mentioned equation. Novel resonant multi-soliton solutions along with their essential conditions were obtained by using simplified LSP, and the conditions guaranteed the existence of resonant solitons. Furthermore, the obtained solutions were used to investigate the dynamic and fission behavior of Y-type multi-soliton waves. For an accurate investigation of physical phenomena, appropriate free parameters were chosen to ascertain the impact on the speed of traveling waves and the initiation time of fission. Three-dimensional and contour plots of the obtained solutions are presented in Figures 1–6. Additionally, two nonlinear equations were formulated and investigated using VR, and the related soliton molecules were simultaneously extracted. The reported resonant Y-type multi-soliton waves and equations are new and have not been previously investigated. They can be used to explain modeled physical phenomena and can provide information about dynamic behavior of shallow water waves.
- simplified linear superposition principle,
- velocity resonance,
- soliton molecule,
- resonant Y-type multi-soliton
Citation: Chun-Ku Kuo, Dipankar Kumar, Chieh-Ju Juan. A study of resonance Y-type multi-soliton solutions and soliton molecules for new (2+1)-dimensional nonlinear wave equations[J]. AIMS Mathematics, 2022, 7(12): 20740-20751. doi: 10.3934/math.20221136

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Abstract

In this study, a fourth-order nonlinear wave equation with variable coefficients was investigated. Through appropriate choice of the free parameters and using the simplified linear superposition principle (LSP) and velocity resonance (VR), the examined equation can be considered as Hirota–Satsuma–Ito, Calogero–Bogoyavlenskii–Schiff and Jimbo–Miwa equations. The main objective of this study was to obtain novel resonant multi-soliton solutions and investigate inelastic interactions of traveling waves for the above-mentioned equation. Novel resonant multi-soliton solutions along with their essential conditions were obtained by using simplified LSP, and the conditions guaranteed the existence of resonant solitons. Furthermore, the obtained solutions were used to investigate the dynamic and fission behavior of Y-type multi-soliton waves. For an accurate investigation of physical phenomena, appropriate free parameters were chosen to ascertain the impact on the speed of traveling waves and the initiation time of fission. Three-dimensional and contour plots of the obtained solutions are presented in Figures 1–6. Additionally, two nonlinear equations were formulated and investigated using VR, and the related soliton molecules were simultaneously extracted. The reported resonant Y-type multi-soliton waves and equations are new and have not been previously investigated. They can be used to explain modeled physical phenomena and can provide information about dynamic behavior of shallow water waves.

References

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