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

AIMS Mathematics

Junjie Li¹  Gurpreet Singh²  Onur Alp İlhan³  Jalil Manafian⁴  Yusif S. Gasimov⁵ 

[1] 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;

关键词: multiple exp-function method;    generalized kadomtsev-petviashvili equation;    modulation instability;    semi-inverse variational principle;   

DOI  :  10.3934/math.2021441

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown