Bilinear Form andN-Shock-Wave Solutions for a (2+1)-Dimensional Breaking Soliton Equation in Certain Fluids with the Bell Polynomials and Auxiliary Function

2013 ◽  
Vol 131 (4) ◽  
pp. 331-342 ◽  
Author(s):  
Yan Jiang ◽  
Bo Tian ◽  
Min Li ◽  
Pan Wang
Keyword(s):  
Shock Wave ◽  
Bilinear Form ◽  
Auxiliary Function ◽  
Bell Polynomials ◽  
Soliton Equation ◽  
Wave Solutions

The lump, lumpoff and rouge wave solutions of a (3+1)-dimensional generalized shallow water wave equation

2019 ◽  
Vol 33 (17) ◽  
pp. 1950190
Author(s):  
Jin-Jie Yang ◽  
Shou-Fu Tian ◽  
Wei-Qi Peng ◽  
Zhi-Qiang Li ◽  
Tian-Tian Zhang
Keyword(s):  
Shallow Water ◽  
Bilinear Form ◽  
Water Wave ◽  
Rational Solution ◽  
Bell Polynomials ◽  
Ocean Engineering ◽  
Shallow Water Wave ◽  
Propagation Behavior ◽  
Wave Solutions ◽  
Lump Wave

We consider the (3[Formula: see text]+[Formula: see text]1)-dimensional generalized shallow water wave (GSWW) equation. By virtue of the binary Bell polynomials theory, we obtain the bilinear form of the equation. Then its lump wave solutions, a kind of rational solution localized in all directions of the space, are derived by employing its bilinear form at the special situation for [Formula: see text]. Furthermore, it is worth noting that the lump wave solutions can interact with single-stripe soliton waves and double-stripe solution waves to generate lumpoff waves and a kind of predictable rouge waves, respectively. Especially, it is interesting that we can predict when and where the peculiar rouge waves will occur. Moreover, in order to understand the dynamics and propagation of the lump waves and the interaction solution, some graphic analyses are exhibited by selecting special parameters. The results of this work can be used to understand the propagation behavior of these solutions of the GSWW equation, which is of great significance for ocean engineering.

scholarly journals Nematic Dispersive Shock Waves from Nonlocal to Local

2021 ◽  
Vol 11 (11) ◽  
pp. 4736
Author(s):  
Saleh Baqer ◽  
Dimitrios J. Frantzeskakis ◽  
Theodoros P. Horikis ◽  
Côme Houdeville ◽  
Timothy R. Marchant ◽  
...  
Keyword(s):  
Shock Wave ◽  
Liquid Crystals ◽  
Shock Waves ◽  
Numerical Solutions ◽  
Wave Structure ◽  
Beam Power ◽  
Input Beam ◽  
Shock Wave Structure ◽  
Wave Solutions ◽  
Modulation Theory

The structure of optical dispersive shock waves in nematic liquid crystals is investigated as the power of the optical beam is varied, with six regimes identified, which complements previous work pertinent to low power beams only. It is found that the dispersive shock wave structure depends critically on the input beam power. In addition, it is known that nematic dispersive shock waves are resonant and the structure of this resonance is also critically dependent on the beam power. Whitham modulation theory is used to find solutions for the six regimes with the existence intervals for each identified. These dispersive shock wave solutions are compared with full numerical solutions of the nematic equations, and excellent agreement is found.

THE EXACT TRAVELING WAVE SOLUTIONS AND THEIR BIFURCATIONS IN THE GARDNER AND GARDNER–KP EQUATIONS

2012 ◽  
Vol 22 (05) ◽  
pp. 1250126 ◽  
Author(s):  
FANG YAN ◽  
CUNCAI HUA ◽  
HAIHONG LIU ◽  
ZENGRONG LIU
Keyword(s):  
Traveling Wave ◽  
Function Method ◽  
Traveling Wave Solutions ◽  
Analytic Solutions ◽  
Auxiliary Function ◽  
Kp Equation ◽  
Gardner Equation ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Kp Equations

By using the method of dynamical systems, this paper studies the exact traveling wave solutions and their bifurcations in the Gardner equation. Exact parametric representations of all wave solutions as well as the explicit analytic solutions are given. Moreover, several series of exact traveling wave solutions of the Gardner–KP equation are obtained via an auxiliary function method.

Lump and interactional solutions of the (2+1)-dimensional generalized breaking soliton equation

2019 ◽  
Vol 34 (03) ◽  
pp. 2050037
Author(s):  
Yu-Pei Fan ◽  
Ai-Hua Chen
Keyword(s):  
Solitary Wave ◽  
Asymptotic Analysis ◽  
Bilinear Form ◽  
Lump Solution ◽  
Soliton Equation ◽  
Long Wave ◽  
Wave Limit

In this paper, by using the long wave limit method, we study lump solution and interactional solution of the (2[Formula: see text]+[Formula: see text]1)-dimensional generalized breaking soliton equation without using bilinear form. The moving properties of the lump solution, and the interactional properties of a lump and a solitary wave, are analyzed theoretically and graphically with asymptotic analysis.

scholarly journals Multiple Lump Solutions of the (4+1)-Dimensional Fokas Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Hongcai Ma ◽  
Yunxiang Bai ◽  
Aiping Deng
Keyword(s):  
Symbolic Computation ◽  
Bilinear Form ◽  
Three Dimensional ◽  
Structural Features ◽  
Computation Method ◽  
Lump Solutions ◽  
Wave Solutions ◽  
Lump Wave

In this paper, we investigate multiple lump wave solutions of the new (4+1)-dimensional Fokas equation by adopting a symbolic computation method. We get its 1-lump solutions, 3-lump solutions, and 6-lump solutions by using its bilinear form. Moreover, some basic characters and structural features of multiple lump waves are explained by depicting the three-dimensional plots.

Sign in / Sign up

Export Citation Format

Share Document