Modulational instability, multiple Exp-function method, SIVP, solitary and cross-kink solutions for the generalized KP equation

Junjie Li; Gurpreet Singh; Onur Alp İlhan; Jalil Manafian; Yusif S. Gasimov; Junjie Li; Gurpreet Singh; Onur Alp İlhan; Jalil Manafian; Yusif S. Gasimov

doi:10.3934/math.2021441

AIMS Mathematics

2021, Volume 6, Issue 7: 7555-7584. doi: 10.3934/math.2021441

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Research article

Modulational instability, multiple Exp-function method, SIVP, solitary and cross-kink solutions for the generalized KP equation

1.
School of Applied Mathematics, Xiamen University of Technology, Xiamen 361024, China
2.
Department of Mathematics, Sant Baba Bhag Singh University, Jalandhar(INDIA)-144030
3.
Department of Mathematics, Faculty of Education, Erciyes University, 38039-Melikgazi-Kayseri, Turkey
4.
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
5.
Natural Sciences Faculty, Lankaran State University, 50, H. Aslanov str., Lankaran, Azerbaijan
6.
Azerbaijan University, J. Hajibeyli, 71, AZ1007, Baku, Azerbaijan
7.
Baku State University, Institute for Physical Problems, Z.Khalilov, 23, AZ1148, Baku, Azerbaijan
8.
Baku State University, Institute of Mathematics and Mechanics, ANAS, B.Vahabzade, 9, AZ1148, Baku, Azerbaijan

Received: 03 February 2021 Accepted: 25 April 2021 Published: 08 May 2021
MSC : 35A20, 35A24, 35A25, 35B10, 70K50

The multiple Exp-function method is employed for seeking the multiple soliton solutions to the generalized (3+1)-dimensional Kadomtsev-Petviashvili (gKP) equation, where contains one-wave, two-wave, and triple-wave solutions. The periodic wave including (exponential, $ \cosh $ hyperbolic, and $ \cos $ periodic), cross-kink containing (exponential, $ \sinh $ hyperbolic, and $ \sin $ periodic), and solitary containing (exponential, $ \tanh $ hyperbolic, and $ \tan $ periodic) wave solutions are obtained. In continuing, the modulation instability is engaged to discuss the stability of obtained solutions. Also, the semi-inverse variational principle is applied for the gKP equation with four major cases. The physical phenomena of these received multiple soliton solutions are analyzed and demonstrated in figures by choosing the specific parameters. By means of symbolic computation these analytical solutions and corresponding rogue waves are obtained with the help of Maple software. Via various three-dimensional, curve, and density charts, dynamical characteristics of these waves are exhibited.
- multiple Exp-function method,
- generalized Kadomtsev-Petviashvili equation,
- modulation instability,
- semi-inverse variational principle
Citation: Junjie Li, Gurpreet Singh, Onur Alp İlhan, Jalil Manafian, Yusif S. Gasimov. Modulational instability, multiple Exp-function method, SIVP, solitary and cross-kink solutions for the generalized KP equation[J]. AIMS Mathematics, 2021, 6(7): 7555-7584. doi: 10.3934/math.2021441

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Abstract

The multiple Exp-function method is employed for seeking the multiple soliton solutions to the generalized (3+1)-dimensional Kadomtsev-Petviashvili (gKP) equation, where contains one-wave, two-wave, and triple-wave solutions. The periodic wave including (exponential, $ \cosh $ hyperbolic, and $ \cos $ periodic), cross-kink containing (exponential, $ \sinh $ hyperbolic, and $ \sin $ periodic), and solitary containing (exponential, $ \tanh $ hyperbolic, and $ \tan $ periodic) wave solutions are obtained. In continuing, the modulation instability is engaged to discuss the stability of obtained solutions. Also, the semi-inverse variational principle is applied for the gKP equation with four major cases. The physical phenomena of these received multiple soliton solutions are analyzed and demonstrated in figures by choosing the specific parameters. By means of symbolic computation these analytical solutions and corresponding rogue waves are obtained with the help of Maple software. Via various three-dimensional, curve, and density charts, dynamical characteristics of these waves are exhibited.

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