Variety interaction between k-lump and k-kink solutions for the generalized Burgers equation with variable coefficients by bilinear analysis
In this paper, we study the generalized Burgers equation with variable coefficients which is considered in soliton theory and generated by considering the Hirota bilinear operators. We retrieve some novel exact analytical solutions, including 2-lump-type wave solutions, interaction between 2-lump an...
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doaj-2af0a2fba8a24c46a46bd5285354a96f2021-08-28T04:43:35ZengElsevierResults in Physics2211-37972021-09-0128104490Variety interaction between k-lump and k-kink solutions for the generalized Burgers equation with variable coefficients by bilinear analysisZiqiang Li0Jalil Manafian1Natig Ibrahimov2Afandiyeva Hajar3Kottakkaran Sooppy Nisar4Wasim Jamshed5School of Mathematics, Zhengzhou University of Aeronautics, Zhengzhou, Henan 450046, ChinaDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran; Natural Sciences Faculty, Lankaran State University, 50, H. Aslanov str., Lankaran, Azerbaijan; Corresponding author.Natural Sciences Faculty, Lankaran State University, 50, H. Aslanov str., Lankaran, AzerbaijanDepartment of Mathematical Economics, Baku State University, Baku, AzerbaijanDepartment of Mathematics, College of Arts and Sciences, Wadi Aldawaser, 11991, Prince Sattam bin Abdulaziz University, Saudi ArabiaDepartment of Mathematics, Capital University of Science and Technology (CUST), Islamabad 44000, PakistanIn this paper, we study the generalized Burgers equation with variable coefficients which is considered in soliton theory and generated by considering the Hirota bilinear operators. We retrieve some novel exact analytical solutions, including 2-lump-type wave solutions, interaction between 2-lump and one kink wave solutions, interaction between two lump and two kink wave solutions, interaction between two lump and two kink wave solutions of another type, interaction between two lump and one periodic wave solutions, interaction between two lump and kink-periodic wave solutions, and interaction between two lump and periodic-periodic wave solutions for the generalized Burgers equation by Maple symbolic computations. The required conditions of the analyticity and positivity of the solutions can be easily achieved by taking special choices of the involved parameters. The main ingredients for this scheme are to recover the Hirota bilinear forms and their generalized equivalences. Through the way of resetting different space constants, we adjust the coordinates of kink-type waves in order for them colliding with the breather wave, after that, the transformed kink-type waves gradually swallow the breather wave. Lastly, the graphical simulations of the exact solutions are depicted.http://www.sciencedirect.com/science/article/pii/S2211379721006021k-lump and k-kink solutionsHirota bilinear operator methodThe generalized Burgers equationMulti-dimensional binary Bell polynomials |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Ziqiang Li Jalil Manafian Natig Ibrahimov Afandiyeva Hajar Kottakkaran Sooppy Nisar Wasim Jamshed |
spellingShingle |
Ziqiang Li Jalil Manafian Natig Ibrahimov Afandiyeva Hajar Kottakkaran Sooppy Nisar Wasim Jamshed Variety interaction between k-lump and k-kink solutions for the generalized Burgers equation with variable coefficients by bilinear analysis Results in Physics k-lump and k-kink solutions Hirota bilinear operator method The generalized Burgers equation Multi-dimensional binary Bell polynomials |
author_facet |
Ziqiang Li Jalil Manafian Natig Ibrahimov Afandiyeva Hajar Kottakkaran Sooppy Nisar Wasim Jamshed |
author_sort |
Ziqiang Li |
title |
Variety interaction between k-lump and k-kink solutions for the generalized Burgers equation with variable coefficients by bilinear analysis |
title_short |
Variety interaction between k-lump and k-kink solutions for the generalized Burgers equation with variable coefficients by bilinear analysis |
title_full |
Variety interaction between k-lump and k-kink solutions for the generalized Burgers equation with variable coefficients by bilinear analysis |
title_fullStr |
Variety interaction between k-lump and k-kink solutions for the generalized Burgers equation with variable coefficients by bilinear analysis |
title_full_unstemmed |
Variety interaction between k-lump and k-kink solutions for the generalized Burgers equation with variable coefficients by bilinear analysis |
title_sort |
variety interaction between k-lump and k-kink solutions for the generalized burgers equation with variable coefficients by bilinear analysis |
publisher |
Elsevier |
series |
Results in Physics |
issn |
2211-3797 |
publishDate |
2021-09-01 |
description |
In this paper, we study the generalized Burgers equation with variable coefficients which is considered in soliton theory and generated by considering the Hirota bilinear operators. We retrieve some novel exact analytical solutions, including 2-lump-type wave solutions, interaction between 2-lump and one kink wave solutions, interaction between two lump and two kink wave solutions, interaction between two lump and two kink wave solutions of another type, interaction between two lump and one periodic wave solutions, interaction between two lump and kink-periodic wave solutions, and interaction between two lump and periodic-periodic wave solutions for the generalized Burgers equation by Maple symbolic computations. The required conditions of the analyticity and positivity of the solutions can be easily achieved by taking special choices of the involved parameters. The main ingredients for this scheme are to recover the Hirota bilinear forms and their generalized equivalences. Through the way of resetting different space constants, we adjust the coordinates of kink-type waves in order for them colliding with the breather wave, after that, the transformed kink-type waves gradually swallow the breather wave. Lastly, the graphical simulations of the exact solutions are depicted. |
topic |
k-lump and k-kink solutions Hirota bilinear operator method The generalized Burgers equation Multi-dimensional binary Bell polynomials |
url |
http://www.sciencedirect.com/science/article/pii/S2211379721006021 |
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