Lump solitons and the interaction phenomena of them for two classes of nonlinear evolution equations

Tang, Yaning; Tao, Siqiao; Guan, Qing

doi:10.1016/j.camwa.2016.08.027

Cited by 154 publications

(43 citation statements)

References 24 publications

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“…The obtained result enriches the existing studies on the (2+1)-dimensional Bogoyavlensky-Konopelchenko equation [19][20][21][22]. We remark that there are plenty of interaction solutions to integrable equations (see, e.g., [31]), particularly between lumps and other kinds of exact solutions to (2+1)dimensional nonlinear integrable equations (see, e.g., [32][33][34][35] for lump-kink interaction solutions and [36][37][38][39] for lumpsoliton interaction solutions).…”

Section: Discussionsupporting

confidence: 79%

Exact Solutions to a Generalized Bogoyavlensky‐Konopelchenko Equation via Maple Symbolic Computations

Chen

2019

Complexity

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We aim to construct exact and explicit solutions to a generalized Bogoyavlensky-Konopelchenko equation through the Maple computer algebra system. The considered nonlinear equation is transformed into a Hirota bilinear form, and symbolic computations are made for solving both the nonlinear equation and the corresponding bilinear equation. A few classes of exact and explicit solutions are generated from different ansätze on solution forms, including traveling wave solutions, two-wave solutions, and polynomial solutions.

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Section: Discussionsupporting

confidence: 79%

Exact Solutions to a Generalized Bogoyavlensky‐Konopelchenko Equation via Maple Symbolic Computations

Chen

2019

Complexity

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“…In this context, many nonlinear evolutions equations which represent many important phenomena have been studied and one investigated its properties and dynamical behavior such as by the Benjamin [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Analytical, semi-analytical, and numerical solutions for the Cahn–Allen equation

Khater

Park

et al. 2020

Adv Differ Equ

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This paper studies the analytical, semi-analytical, and numerical solutions of the Cahn-Allen equation, which plays a vital role in describing the structure of the dynamics for phase separation in Fe-Cr-X (X = Mo, Cu) ternary alloys. The modified Khater method, the Adomian decomposition method, and the quintic B-spline scheme are implemented on our suggested model to get distinct kinds of solutions. These solutions describe the dynamics of the phase separation in iron alloys and are also used in solidification and nucleation problems. The applications of this model arise in many various fields such as plasma physics, quantum mechanics, mathematical biology, and fluid dynamics. The comparison between the obtained solutions is represented by using figures and tables to explain the value of the error between exact and numerical solutions. All solutions are verified by using Mathematica software.

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“…Fokas et al studied the completely elastic collision between a lump wave and a line soliton of the DSII equation [30]. Tang et al investigated the nonelastic collision between a lump wave and a stripe soliton of the (2+1)-dimensional Ito equation [31]. Then the interaction lump-soliton solutions [32,33], lump-twin-stripe solutions [34], and lump-periodic wave solutions [35] were investigated.…”

Section: Introductionmentioning

confidence: 99%

Rogue Wave and Multiple Lump Solutions of the (2+1)‐Dimensional Benjamin‐Ono Equation in Fluid Mechanics

Zhao

Gao

2019

Complexity

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In this paper, the bilinear method is employed to investigate the rogue wave solutions and the rogue type multiple lump wave solutions of the (2+1)-dimensional Benjamin-Ono equation. Two theorems for constructing rogue wave solutions are proposed with the aid of a variable transformation. Four kinds of rogue wave solutions are obtained by means of Theorem 1. In Theorem 2, three polynomial functions are used to derive multiple lump wave solutions. The 3-lump solutions, 6-lump solutions, and 8lump solutions are presented, respectively. The 3-lump wave has a "triangular" structure. The centers of the 6-lump wave form a pentagram around a single lump wave. The 8-lump wave consists of a set of seven first order rogue waves and one second order rogue wave as the center. The multiple lump wave develops into low order rogue wave as parameters decline to zero. The method presented in this paper provides a uniform method for investigating high order rational solutions. All the results are useful in explaining high dimensional dynamical phenomena of the (2+1)-dimensional Benjamin-Ono equation.

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Lump solitons and the interaction phenomena of them for two classes of nonlinear evolution equations

Cited by 154 publications

References 24 publications

Exact Solutions to a Generalized Bogoyavlensky‐Konopelchenko Equation via Maple Symbolic Computations

Exact Solutions to a Generalized Bogoyavlensky‐Konopelchenko Equation via Maple Symbolic Computations

Analytical, semi-analytical, and numerical solutions for the Cahn–Allen equation

Rogue Wave and Multiple Lump Solutions of the (2+1)‐Dimensional Benjamin‐Ono Equation in Fluid Mechanics

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