scholarly journals Solitary waves, homoclinic breather waves and rogue waves of the (3+1)-dimensional Hirota bilinear equation

2018 ◽  
Vol 75 (3) ◽  
pp. 957-964 ◽  
Author(s):  
Min-Jie Dong ◽  
Shou-Fu Tian ◽  
Xue-Wei Yan ◽  
Li Zou
Keyword(s):  
Solitary Waves ◽  
Rogue Waves ◽  
Hirota Bilinear Equation ◽  
Hirota Bilinear ◽  
Bilinear Equation

scholarly journals A Hirota bilinear equation for Painlevé transcendents PIV, PII and PI

2018 ◽  
Vol 07 (04) ◽  
pp. 1840001
Author(s):  
A. N. W. Hone ◽  
F. Zullo
Keyword(s):  
Taylor Series ◽  
Taylor Expansion ◽  
Tau Function ◽  
Tau Functions ◽  
Sigma Function ◽  
Special Cases ◽  
Hirota Bilinear Equation ◽  
Order Four ◽  
Hirota Bilinear ◽  
Bilinear Equation

We present some observations on the tau-function for the fourth Painlevé equation. By considering a Hirota bilinear equation of order four for this tau-function, we describe the general form of the Taylor expansion around an arbitrary movable zero. The corresponding Taylor series for the tau-functions of the first and second Painlevé equations, as well as that for the Weierstrass sigma function, arise naturally as special cases, by setting certain parameters to zero.

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.

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

Solitary waves, rogue waves and homoclinic breather waves for a (2 + 1)-dimensional generalized Kadomtsev–Petviashvili equation

2017 ◽  
Vol 31 (30) ◽  
pp. 1750281 ◽  
Author(s):  
Min-Jie Dong ◽  
Shou-Fu Tian ◽  
Xue-Wei Yan ◽  
Li Zou ◽  
Jin Li
Keyword(s):  
Solitary Waves ◽  
Bilinear Form ◽  
Dynamical Behavior ◽  
Rogue Waves ◽  
Liquid Drops ◽  
Petviashvili Equation ◽  
Bell’S Polynomials ◽  
Bilinear Equation

We study a (2 + 1)-dimensional generalized Kadomtsev–Petviashvili (gKP) equation, which characterizes the formation of patterns in liquid drops. By using Bell’s polynomials, an effective way is employed to succinctly construct the bilinear form of the gKP equation. Based on the resulting bilinear equation, we derive its solitary waves, rogue waves and homoclinic breather waves, respectively. Our results can help enrich the dynamical behavior of the KP-type equations.

A New $$(3+1)$$-dimensional Hirota Bilinear Equation: Its Bäcklund Transformation and Rational-type Solutions

2020 ◽  
Vol 25 (4) ◽  
pp. 383-391 ◽  
Author(s):  
Kamyar Hosseini ◽  
Majid Samavat ◽  
Mohammad Mirzazadeh ◽  
Wen-Xiu Ma ◽  
Zakia Hammouch
Keyword(s):  
Bäcklund Transformation ◽  
Backlund Transformation ◽  
Hirota Bilinear Equation ◽  
Hirota Bilinear ◽  
Rational Type ◽  
Bilinear Equation
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