General high–order breathers and rogue waves in the(3+1)-dimensional KP–Boussinesq equation

2018 ◽  
Vol 64 ◽  
pp. 1-13 ◽  
Author(s):  
Baonan Sun ◽  
Abdul-Majid Wazwaz
Keyword(s):  
Boussinesq Equation ◽  
Rogue Waves ◽  
High Order

Novel high‐order breathers and rogue waves in the Boussinesq equation via determinants

2019 ◽  
Vol 43 (6) ◽  
pp. 3701-3715 ◽  
Author(s):  
Yunkai Liu ◽  
Biao Li ◽  
Abdul‐Majid Wazwaz
Keyword(s):  
Boussinesq Equation ◽  
Rogue Waves ◽  
High Order

Analytic rogue wave-type solutions for the generalized (2+1)-dimensional Boussinesq Equation

2021 ◽  
pp. 2150380
Author(s):  
Xiu-Rong Guo
Keyword(s):  
Boussinesq Equation ◽  
Rogue Wave ◽  
Wave Interaction ◽  
Rogue Waves ◽  
Rational Solutions ◽  
Wave Type ◽  
Hirota Bilinear Form ◽  
Basic Facts ◽  
2D And 3D ◽  
Solitary Wave Interaction

Based on the Hirota bilinear form of the generalized (2+1)-dimensional Boussinesq equation, which can be expressed as the shallow water wave mechanism appearing in fluid mechanics, we applied the new polynomial functions to construct the rational solutions and rogue wave-type solutions. Next, the system parameters control on the rational solutions and rogue wave-type solutions were also shown. As a result, we found the following basic facts: (i) these parameters may affect the wave shapes, amplitude, and bright/dark for this considered equation, (ii) the solitary wave interaction rogue waves and triplet rogue wave-type solutions can be viewed on [Formula: see text], [Formula: see text], and [Formula: see text] planes, respectively. Their nonlinear dynamic behaviors were presented by numerical simulation of the 2D- and 3D-plots.

scholarly journals General Rogue Waves in the Boussinesq Equation

2020 ◽  
Vol 89 (2) ◽  
pp. 024003 ◽  
Author(s):  
Bo Yang ◽  
Jianke Yang
Keyword(s):  
Boussinesq Equation ◽  
Rogue Waves

Characteristics of the breathers, rogue waves and solitary waves in a generalized (2+1)-dimensional Boussinesq equation

2016 ◽  
Vol 115 (1) ◽  
pp. 10002 ◽  
Author(s):  
Xiu-Bin Wang ◽  
Shou-Fu Tian ◽  
Chun-Yan Qin ◽  
Tian-Tian Zhang
Keyword(s):  
Solitary Waves ◽  
Boussinesq Equation ◽  
Rogue Waves

Rogue Waves and Hybrid Solutions of the Boussinesq Equation

2017 ◽  
Vol 72 (4) ◽  
pp. 307-314 ◽  
Author(s):  
Ji-Guang Rao ◽  
Yao-Bin Liu ◽  
Chao Qian ◽  
Jing-Song He
Keyword(s):  
Boussinesq Equation ◽  
Rogue Wave ◽  
Three Dimensional ◽  
Rogue Waves ◽  
Rational Solutions ◽  
Bilinear Method ◽  
Long Wave ◽  
Hybrid Solutions ◽  
Wave Limit ◽  
Hirota Bilinear

AbstractThe rational and semirational solutions in the Boussinesq equation are obtained by the Hirota bilinear method and long wave limit. It is shown that the rational solutions contain dark and bright rogue waves, and their typical dynamics are analysed and illustrated. The semirational solutions possess a range of hybrid solutions, and the hybrid of rogue wave and solitons are demonstrated in detail by the three-dimensional figures. Under certain parameter conditions, a new kind of semirational solutions consisted of rogue waves, breathers and solitons is discovered, which describes the dynamics of the rogue waves interacting with the breathers and solitons at the same time.

High Order Energy-Preserving Method of the “Good” Boussinesq Equation

2016 ◽  
Vol 9 (1) ◽  
pp. 111-122 ◽  
Author(s):  
Chaolong Jiang ◽  
Jianqiang Sun ◽  
Xunfeng He ◽  
Lanlan Zhou
Keyword(s):  
Vector Field ◽  
Fourth Order ◽  
Boussinesq Equation ◽  
Field Method ◽  
High Order ◽  
Discrete Energy ◽  
High Order Scheme ◽  
Order Energy ◽  
Order Scheme ◽  
Pseudo Spectral Method

AbstractThe fourth order average vector field (AVF) method is applied to solve the “Good” Boussinesq equation. The semi-discrete system of the “good” Boussinesq equation obtained by the pseudo-spectral method in spatial variable, which is a classical finite dimensional Hamiltonian system, is discretizated by the fourth order average vector field method. Thus, a new high order energy conservation scheme of the “good” Boussinesq equation is obtained. Numerical experiments confirm that the new high order scheme can preserve the discrete energy of the “good” Boussinesq equation exactly and simulate evolution of different solitary waves well.

High-order rogue waves of the Benjamin–Ono equation and the nonlocal nonlinear Schrödinger equation

2017 ◽  
Vol 31 (29) ◽  
pp. 1750269 ◽  
Author(s):  
Wei Liu
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Nonlinear Schrodinger Equation ◽  
High Order ◽  
Wave Patterns ◽  
Nonlocal Nonlinear Schrödinger Equation ◽  
Nonlocal Nonlinear

High-order rogue wave solutions of the Benjamin–Ono equation and the nonlocal nonlinear Schrödinger equation are derived by employing the bilinear method, which are expressed by simple polynomials. Typical dynamics of these high-order rogue waves are studied by analytical and graphical ways. For the Benjamin–Ono equation, there are two types of rogue waves, namely, bright rogue waves and dark rogue waves. In particular, the fundamental rogue wave pattern is different from the usual fundamental rogue wave patterns in other soliton equations. For the nonlocal nonlinear Schrödinger equation, the exact explicit rogue wave solutions up to the second order are presented. Typical rogue wave patterns such as Peregrine-type, triple and fundamental rogue waves are put forward. These high-order rogue wave patterns have not been shown before in the nonlocal Schrödinger equation.

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