N-Solitons, kink and periodic wave solutions for (3 + 1)-dimensional Hirota bilinear equation using three distinct techniques

2019 ◽  
Vol 60 ◽  
pp. 48-60 ◽  
Author(s):  
S.M. Mabrouk ◽  
A.S. Rashed
Keyword(s):  
Periodic Wave ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Hirota Bilinear Equation ◽  
Hirota Bilinear ◽  
Bilinear Equation

Lump-type solutions, interaction solutions and periodic wave solutions of a (3+1)-dimensional Korteweg–de Vries equation

2019 ◽  
Vol 33 (27) ◽  
pp. 1950319 ◽  
Author(s):  
Hongfei Tian ◽  
Jinting Ha ◽  
Huiqun Zhang
Keyword(s):  
Vries Equation ◽  
Kdv Equation ◽  
Periodic Wave ◽  
Periodic Wave Solutions ◽  
Interaction Solutions ◽  
Dynamical Behaviors ◽  
Wave Solutions ◽  
Hirota Bilinear Form ◽  
De Vries ◽  
Hirota Bilinear

Based on the Hirota bilinear form, lump-type solutions, interaction solutions and periodic wave solutions of a (3[Formula: see text]+[Formula: see text]1)-dimensional Korteweg–de Vries (KdV) equation are obtained. The interaction between a lump-type soliton and a stripe soliton including two phenomena: fission and fusion, are illustrated. The dynamical behaviors are shown more intuitively by graphics.

EXACT SOLITON SOLUTIONS AND QUASI-PERIODIC WAVE SOLUTIONS TO THE FORCED VARIABLE-COEFFICIENT KdV EQUATION

2012 ◽  
Vol 26 (19) ◽  
pp. 1250072 ◽  
Author(s):  
YI ZHANG ◽  
ZHILONG CHENG
Keyword(s):  
Variable Coefficient ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Periodic Wave ◽  
Time Dependent ◽  
Bilinear Method ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Hirota Bilinear ◽  
Exact Soliton Solutions

In this paper, the time-dependent variable-coefficient KdV equation with a forcing term is considered. Based on the Hirota bilinear method, the bilinear form of this equation is obtained, and the multi-soliton solutions are studied. Then the periodic wave solutions are obtained by using Riemann theta function, and it is also shown that classical soliton solutions can be reduced from the periodic wave solutions.

RIEMANN THETA FUNCTIONS SOLUTIONS WITH RATIONAL CHARACTERISTICS FOR (2+1)-DIMENSIONAL SINH-GORDON EQUATION

2010 ◽  
Vol 24 (06) ◽  
pp. 575-584
Author(s):  
YANG FENG ◽  
HONG-QING ZHANG
Keyword(s):  
Gordon Equation ◽  
Theta Functions ◽  
Periodic Wave ◽  
Bilinear Method ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Wave Numbers ◽  
Riemann Theta Functions ◽  
The Waves ◽  
Hirota Bilinear

In this letter, we use the Riemann theta functions with rational characteristics and the Hirota bilinear method to construct quasi-periodic wave solutions for (2+1)-dimensional sinh-Gordon equation. This method not only conveniently obtains quasi-periodic solutions of nonlinear equations, but also directly gets the explicit expressions of frequencies, wave numbers, phase and amplitudes for the waves.

scholarly journals Rational wave solutions to a generalized (2+1)-dimensional Hirota bilinear equation

2020 ◽  
Vol 15 ◽  
pp. 61 ◽  
Author(s):  
K. Hosseini ◽  
M. Mirzazadeh ◽  
M. Aligoli ◽  
M. Eslami ◽  
J.G. Liu
Keyword(s):  
Nonlinear Waves ◽  
Soliton Solutions ◽  
Wave Solutions ◽  
Multiple Soliton Solutions ◽  
Simplified Hirota’S Method ◽  
Complexiton Solutions ◽  
Hirota Bilinear Equation ◽  
Different Types ◽  
Hirota Bilinear ◽  
Bilinear Equation

A generalized form of (2+1)-dimensional Hirota bilinear (2D-HB) equation is considered herein in order to study nonlinear waves in fluids and oceans. The present goal is carried out through adopting the simplified Hirota’s method as well as ansatz approaches to retrieve a bunch of rational wave structures from multiple soliton solutions to breather, rational, and complexiton solutions. Some figures corresponding to a series of rational wave structures are provided, illustrating the dynamics of the obtained solutions. The results of the present paper help to reveal the existence of rational wave structures of different types for the 2D-HB equation.

Abundant interaction between lump and k-kink, periodic and other analytical solutions for the (3+1)-D Burger system by bilinear analysis

2021 ◽  
Vol 35 (13) ◽  
pp. 2150173
Author(s):  
Na Zhao ◽  
Jalil Manafian ◽  
Onur Alp Ilhan ◽  
Gurpreet Singh ◽  
Rana Zulfugarova
Keyword(s):  
Analytical Solutions ◽  
Periodic Wave ◽  
Bell Polynomials ◽  
Solitary Wave Solutions ◽  
Soliton Theory ◽  
Periodic Wave Solutions ◽  
Bilinear Operators ◽  
Wave Solutions ◽  
Kink Wave ◽  
Hirota Bilinear

In this paper, we study the (3+1)-dimensional Burger system which is considered in soliton theory and generated by considering the Hirota bilinear operators. The bilinear frame to the Burger system by using the multi-dimensional Bell polynomials is constructed. Also, based on the binary Bäcklund transformations, the generalized Bell polynomials are written. We retrieve some novel exact analytical solutions, containing interaction between lump and two kink wave solutions, interaction between lump and periodic wave solutions, interaction between stripe and periodic solutions, breather wave solutions, cross-kink wave solutions, interaction between kink and periodic wave solutions, multi-wave solutions, and finally solitary wave solutions for the (3+1)-dimensional Burger system 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 trilinear forms and their generalized equivalences.

scholarly journals Resonant behavior of multiple wave solutions to a Hirota bilinear equation

2016 ◽  
Vol 72 (5) ◽  
pp. 1225-1229 ◽  
Author(s):  
Li-Na Gao ◽  
Xue-Ying Zhao ◽  
Yao-Yao Zi ◽  
Jun Yu ◽  
Xing Lü
Keyword(s):  
Multiple Wave ◽  
Wave Solutions ◽  
Hirota Bilinear Equation ◽  
Resonant Behavior ◽  
Hirota Bilinear ◽  
Bilinear Equation

scholarly journals Traveling Wave Solutions and Infinite-Dimensional Linear Spaces of Multiwave Solutions to Jimbo-Miwa Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Lijun Zhang ◽  
C. M. Khalique
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Wave System ◽  
Infinite Dimensional ◽  
Wave Solutions ◽  
Hirota Bilinear Equation ◽  
Periodic Traveling Wave ◽  
Multiwave Solutions ◽  
Hirota Bilinear ◽  
Bilinear Equation

The traveling wave solutions and multiwave solutions to (3 + 1)-dimensional Jimbo-Miwa equation are investigated in this paper. As a result, besides the exact bounded solitary wave solutions, we obtain the existence of two families of bounded periodic traveling wave solutions and their implicit formulas by analysis of phase portrait of the corresponding traveling wave system. We derive the exact 2-wave solutions and two families of arbitrary finiteN-wave solutions by studying the linear space of its Hirota bilinear equation, which confirms that the (3 + 1)-dimensional Jimbo-Miwa equation admits multiwave solutions of any order and is completely integrable.

On quasi-periodic wave solutions and asymptotic behaviors to a (2 + 1)-dimensional generalized variable-coefficient Sawada–Kotera equation

2015 ◽  
Vol 29 (19) ◽  
pp. 1550101 ◽  
Author(s):  
Jian-Min Tu ◽  
Shou-Fu Tian ◽  
Mei-Juan Xu ◽  
Pan-Li Ma
Keyword(s):  
Periodic Solutions ◽  
Variable Coefficient ◽  
Asymptotic Properties ◽  
Soliton Solutions ◽  
Periodic Wave ◽  
Bell Polynomials ◽  
Nonlinear Phenomena ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Bilinear Equation

In this paper, a [Formula: see text]-dimensional generalized variable-coefficient Sawada–Kotera (gvcSK) equation is investigated, which describes many nonlinear phenomena in fluid dynamics and plasma physics. Based on the properties of binary Bell polynomials, we present a Hirota’s bilinear equation to the gvcSK equation. By virtue of the Hirota’s bilinear equation, we obtain the N-soliton solutions and the quasi-periodic wave solutions of the gvcSK equation, which can be reduced to the ones of several integrable equations such as Sawada–Kotera, modified Caudrey–Dodd–Gibbon–Sawada–Kotera, isospectral BKP equations and etc. Furthermore, we obtain the relationship between the soliton solutions and periodic solutions by considering the asymptotic properties of the periodic solutions.

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