Multiple rogue wave, breather wave and interaction solutions of a generalized (3 + 1)-dimensional variable-coefficient nonlinear wave equation

2021 ◽  
Author(s):  
Jian-Guo Liu ◽  
Wen-Hui Zhu
Keyword(s):  
Wave Equation ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Variable Coefficient ◽  
Rogue Wave ◽  
Interaction Solutions ◽  
Dimensional Variable

scholarly journals Lump and Interaction Solutions to the ( 3 + 1 )-Dimensional Variable-Coefficient Nonlinear Wave Equation with Multidimensional Binary Bell Polynomials

2021 ◽  
Vol 2021 ◽  
pp. 1-23
Author(s):  
Xuejun Zhou ◽  
Onur Alp Ilhan ◽  
Fangyuan Zhou ◽  
Sutarto Sutarto ◽  
Jalil Manafian ◽  
...  
Keyword(s):  
Wave Equation ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Variable Coefficient ◽  
Soliton Solutions ◽  
Regularity Of Solutions ◽  
Bell Polynomials ◽  
Soliton Theory ◽  
Dimensional Variable ◽  
Binary Bell Polynomials

In this paper, we study the ( 3 + 1 )-dimensional variable-coefficient nonlinear wave equation which is taken in soliton theory and generated by utilizing the Hirota bilinear technique. We obtain some new exact analytical solutions, containing interaction between a lump-two kink solitons, interaction between two lumps, and interaction between two lumps-soliton, lump-periodic, and lump-three kink solutions for the generalized ( 3 + 1 )-dimensional nonlinear wave equation in liquid with gas bubbles by the Maple symbolic package. Making use of Hirota’s bilinear scheme, we obtain its general soliton solutions in terms of bilinear form equation to the considered model which can be obtained by multidimensional binary Bell polynomials. Furthermore, we analyze typical dynamics of the high-order soliton solutions to show the regularity of solutions and also illustrate their behavior graphically.

Abundant soliton wave solutions for the (3+1)-dimensional variable-coefficient nonlinear wave equation in liquid with gas bubbles by bilinear analysis

2021 ◽  
Author(s):  
Guanqi Tao ◽  
Jalil Manafian ◽  
Onur Alp İlhan ◽  
Syed Maqsood Zia ◽  
Latifa Agamalieva
Keyword(s):  
Wave Equation ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Variable Coefficient ◽  
Soliton Solutions ◽  
Gas Bubbles ◽  
Soliton Theory ◽  
Wave Solutions ◽  
Dimensional Variable ◽  
Hirota Bilinear

In this paper, we check and scan the (3+1)-dimensional variable-coefficient nonlinear wave equation which is considered in soliton theory and generated by considering the Hirota bilinear operators. We retrieve some novel exact analytical solutions, including cross-kink soliton solutions, breather wave solutions, interaction between stripe and periodic, multi-wave solutions, periodic wave solutions and solitary wave solutions for the (3+1)-dimensional variable-coefficient nonlinear wave equation in liquid with gas bubbles 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. Lastly, the graphical simulations of the exact solutions are depicted.

On the global existence and asymptotic behavior of the solution of a nonlinear wave equation with past history

2021 ◽  
Vol 62 (3) ◽  
pp. 031512
Author(s):  
Adel M. Al-Mahdi ◽  
Mohammad M. Al-Gharabli ◽  
Mohammad Kafini ◽  
Shadi Al-Omari
Keyword(s):  
Asymptotic Behavior ◽  
Wave Equation ◽  
Global Existence ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Past History
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