Multiwave interaction solutions for the (3+1)-dimensional extended Jimbo–Miwa equation

2020 ◽  
Vol 34 (35) ◽  
pp. 2050405
Author(s):  
Wenying Cui ◽  
Wei Li ◽  
Yinping Liu
Keyword(s):  
Algebraic Method ◽  
Periodic Waves ◽  
New Techniques ◽  
Interaction Solutions ◽  
Long Wave ◽  
Multiwave Interaction ◽  
Different Types ◽  
Wave Limit ◽  
Solving Strategy ◽  
New Algorithms

In this paper, for the (3+1)-dimensional extended Jimbo–Miwa equation, by the direct algebraic method, together with the inheritance solving strategy, we construct its interaction solutions among solitons, rational waves, and periodic waves. Meanwhile, we construct its interaction solutions among solitons, breathers, and lumps of any higher orders by an [Formula: see text]-soliton decomposition algorithm, together with the parameters conjugated assignment and long-wave limit techniques. The highlight of the paper is that by applying new algorithms and new techniques, we obtained different types of new multiwave interaction solutions for the (3+1)-dimensional extended Jimbo–Miwa equation.

On periodic water-waves and their convergence to solitary waves in the long-wave limit

1981 ◽  
Vol 303 (1481) ◽  
pp. 633-669 ◽  
Keyword(s):  
Integral Equation ◽  
Solitary Waves ◽  
Water Waves ◽  
Periodic Problem ◽  
Existence Theory ◽  
Periodic Waves ◽  
Equation Formulation ◽  
Long Wave ◽  
Integral Equation Formulation ◽  
Wave Limit

A detailed discussion of Nekrasov’s approach to the steady water-wave problems leads to a new integral equation formulation of the periodic problem. This development allows the adaptation of the methods of Amick & Toland (1981) to show the convergence of periodic waves to solitary waves in the long-wave limit. In addition, it is shown how the classical integral equation formulation due to Nekrasov leads, via the Maximum Principle, to new results about qualitative features of periodic waves for which there has long been a global existence theory (Krasovskii 1961, Keady & Norbury 1978).

Lumps, breathers, rogue waves and interaction solutions to a (3+1)-dimensional Kudryashov–Sinelshchikov equation

2020 ◽  
Vol 34 (12) ◽  
pp. 2050117 ◽  
Author(s):  
Xianglong Tang ◽  
Yong Chen
Keyword(s):  
Rogue Waves ◽  
Hirota Bilinear Method ◽  
Bilinear Method ◽  
Lump Solutions ◽  
Interaction Solutions ◽  
Long Wave ◽  
Wave Limit ◽  
Hirota Bilinear

Utilizing the Hirota bilinear method, the lump solutions, the interaction solutions with the lump and the stripe solitons, the breathers and the rogue waves for a (3[Formula: see text]+[Formula: see text]1)-dimensional Kudryashov–Sinelshchikov equation are constructed. Two types of interaction solutions between the lumps and the stripe solitons are exhibited. Some different breathers are given by choosing special parameters in the expressions of the solitons. Through a long wave limit of breathers, the lumps and rogue waves are derived.

Multiwave interaction solutions for a (3 + 1)-dimensional B-type Kadomtsev–Petviashvili equation in fluid dynamics

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Wenying Cui ◽  
Yinping Liu ◽  
Zhibin Li
Keyword(s):  
Fluid Dynamics ◽  
Algebraic Method ◽  
Higher Order ◽  
Decomposition Algorithm ◽  
Periodic Waves ◽  
Order Interaction ◽  
Interaction Solutions ◽  
Petviashvili Equation ◽  
Bkp Equation ◽  
Interaction Phenomena

Abstract In this paper, a (3 + 1)-dimensional B-type Kadomtsev–Petviashvili (BKP) equation is investigated and its various new interaction solutions among solitons, rational waves and periodic waves are obtained by the direct algebraic method, together with the inheritance solving technique. The results are fantastic interaction phenomena, and are shown by figures. Meanwhile, any higher order interaction solutions among solitons, breathers, and lump waves are constructed by an N-soliton decomposition algorithm developed by us. These innovative results greatly enrich the structure of the solutions of this equation.

Soliton molecules and some related interaction solutions of the (2+1)-dimensional Kadomtsev–Petviashvili hierarchy

2020 ◽  
pp. 2150106
Author(s):  
Jiamin Zhu ◽  
Bo Wang ◽  
Zhengyi Ma ◽  
Jinxi Fei
Keyword(s):  
Resonance Condition ◽  
Soliton Solutions ◽  
Elastic Interaction ◽  
Elastic Collision ◽  
Wave Number ◽  
Interaction Solutions ◽  
Long Wave ◽  
Text Interaction ◽  
Wave Limit ◽  
Line Soliton

The [Formula: see text]-soliton solutions of the (2+1)-dimensional Kadomtsev–Petviashvili hierarchy are first constructed. One soliton molecule satisfies the velocity resonance condition, the breather with the periodic solitary wave, the lump soliton localized in all directions in the space are showed successively for [Formula: see text]. Interaction of one soliton molecule and a line soliton, the soliton molecule hybrid a line soliton with the breather/lump soliton are presented for [Formula: see text]. Moreover, the elastic interaction between two-soliton molecules, the interaction between one soliton molecule, and a breather and the elastic collision between the lump soliton and one soliton molecule are also derived for [Formula: see text] by applying the velocity resonance, the module resonance of wave number, and the long-wave limit ideas. Figures are presented to demonstrate these dynamics features.

Diverse solitons and interaction solutions for the (2+1)-dimensional CDGKS equation

2019 ◽  
Vol 33 (16) ◽  
pp. 1950174 ◽  
Author(s):  
Jian-Hong Zhuang ◽  
Yaqing Liu ◽  
Xin Chen ◽  
Juan-Juan Wu ◽  
Xiao-Yong Wen
Keyword(s):  
Soliton Solutions ◽  
Propagation Direction ◽  
Soliton Interaction ◽  
Bilinear Method ◽  
Interaction Solutions ◽  
Dynamical Behaviors ◽  
Long Wave ◽  
Wave Limit ◽  
Hirota Bilinear ◽  
Line Soliton

In this paper, the (2[Formula: see text]+[Formula: see text]1)-dimensional CDGKS equation is studied and its diverse soliton solutions consisting of line soliton, periodic soliton and lump soliton with different parameters are derived based on the Hirota bilinear method and long-wave limit method. Based on exact solution formulae with different parameters, the interaction between line soliton and periodic soliton, the interaction between line soliton and lump soliton, as well as the interaction between periodic soliton and lump soliton are illustrated. According to the dynamical behaviors, it can be found that the effects of different parameters are on the propagation direction and shapes. Novel soliton interaction phenomena are also observed.

scholarly journals Lumps, breathers, and interaction solutions of a (3+1)-dimensional generalized Kadovtsev–Petviashvili equation

2020 ◽  
pp. 2150041
Author(s):  
Xi Ma ◽  
Tie-Cheng Xia ◽  
Handong Guo
Keyword(s):  
Soliton Solution ◽  
Hirota Bilinear Method ◽  
Kp Equation ◽  
Bilinear Method ◽  
Test Technique ◽  
Interaction Solutions ◽  
Long Wave ◽  
Petviashvili Equation ◽  
Wave Limit ◽  
Hirota Bilinear

In this paper, we use the Hirota bilinear method to find the [Formula: see text]-soliton solution of a [Formula: see text]-dimensional generalized Kadovtsev–Petviashvili (KP) equation. Then, we obtain the [Formula: see text]-order breathers of the equation, and combine the long-wave limit method to give the [Formula: see text]-order lumps. Resorting to the extended homoclinic test technique, we obtain the breather-kink solutions for the equation. Last, the interaction solution composed of the [Formula: see text]-soliton solution, [Formula: see text]-breathers, and [Formula: see text]-lumps for the [Formula: see text]-dimensional generalized KP equation is constructed.

scholarly journals Elastic waves in periodically heterogeneous two-dimensional media: locally periodic and anti-periodic modes

2018 ◽  
Vol 474 (2215) ◽  
pp. 20170908
Author(s):  
Igor V. Andrianov ◽  
Vladyslav V. Danishevskyy ◽  
Graham Rogerson
Keyword(s):  
Elastic Waves ◽  
Plane Waves ◽  
Square Lattice ◽  
Periodic Case ◽  
Long Wave ◽  
Fibrous Medium ◽  
Heterogeneous Structures ◽  
Different Types ◽  
Classical Waves ◽  
Wave Limit

Propagation of anti-plane waves through a discrete square lattice and through a continuous fibrous medium is studied. In the long-wave limit, for periodically heterogeneous structures the solution can be periodic or anti-periodic across the unit cell. It is shown that combining periodicity and anti-periodicity conditions in different directions of the translational symmetry allows one to detect different types of modes that do not arise in the purely periodic case. Such modes may be interpreted as counterparts of non-classical waves appearing in phenomenological theories. Dispersion diagrams of the discrete square lattice are evaluated in a closed analytical from. Dispersion properties of the fibrous medium are determined using Floquet–Bloch theory and Fourier series approximations. Influence of a viscous damping is taken into account.

Interaction solutions of the first BKP equation

2019 ◽  
Vol 33 (17) ◽  
pp. 1950191
Author(s):  
Jing Chen ◽  
Jian-Ping Yu ◽  
Wen-Xiu Ma ◽  
Yong-Li Sun ◽  
Chaudry Masood Khalique
Keyword(s):  
Nonlinear Optics ◽  
Dynamic Properties ◽  
Direct Method ◽  
Soliton Solutions ◽  
Nonlinear Problems ◽  
Interaction Solutions ◽  
Long Wave ◽  
Wave Limit ◽  
Bkp Equation

In this paper, we study the interaction solutions of the first BKP equation by using the Hirota direct method and taking long-wave limit. In order to obtain the interaction solutions, the multi-soliton solutions are firstly derived using the Hirota direct method, then the interaction solutions are successfully constructed by properly choosing appropriate parameters and taking long-wave limit on the soliton solutions. These parameters have great influences on the propagation directions, shapes as well as energy. Moreover, the dynamic properties of these obtained solutions are illustrated vividly by some graphs. The results in this work could be used to solve nonlinear problems in nonlinear optics and engineering field.

Nonlocal symmetries, solitary waves and cnoidal periodic waves of the (2+1)-dimensional breaking soliton equation

2017 ◽  
Vol 31 (36) ◽  
pp. 1750348
Author(s):  
Li Zou ◽  
Shou-Fu Tian ◽  
Lian-Li Feng
Keyword(s):  
Solitary Waves ◽  
Expansion Method ◽  
Periodic Waves ◽  
Nonlocal Symmetry ◽  
Soliton Equation ◽  
Nonlocal Symmetries ◽  
Interaction Solutions ◽  
Long Wave ◽  
Truncated Painlevé Expansion ◽  
Consistent Riccati Expansion

In this paper, we consider the (2[Formula: see text]+[Formula: see text]1)-dimensional breaking soliton equation, which describes the interaction of a Riemann wave propagating along the y-axis with a long wave along the x-axis. By virtue of the truncated Painlevé expansion method, we obtain the nonlocal symmetry, Bäcklund transformation and Schwarzian form of the equation. Furthermore, by using the consistent Riccati expansion (CRE), we prove that the breaking soliton equation is solvable. Based on the consistent tan-function expansion, we explicitly derive the interaction solutions between solitary waves and cnoidal periodic waves.

scholarly journals Fission and Fusion Solutions in the (2+1)-Dimensional Generalized Calogero-Bogoyavlenskii-Schiff Equation

2022 ◽  
Author(s):  
Yuhan Li ◽  
Hongli AN ◽  
Yiyuan Zhang
Keyword(s):  
Physical Models ◽  
Complex Conjugation ◽  
Capital Letter ◽  
Interaction Solutions ◽  
Dynamical Behaviors ◽  
Hybrid Resonance ◽  
Long Wave ◽  
Hybrid Solutions ◽  
Wave Limit

Abstract Fission and fusion are important phenomena, which have been observed experimentally in many physical areas. In this paper, we study the above two phenomena in the (2+1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation. By introducing some new constraint conditions to its N-solitons, the fifission and fusion are obtained. Numerical figures show that the two types of solutions look like the capital letter Y in spacial structures. Then, by taking a long wave limit approach and complex conjugation restrictions, some hybrid resonance solutions are generated, such as the interaction solutions between the L-order lumps and Q-fifission (fusion) solitons, as well as hybrid solutions mixed by the T-order breathers and Q-fifission (fusion) solitons. Dynamical behaviors of these solutions are analyzed theoretically and numerically. The results obtained can be helpful for understanding the fusion and fifission phenomena in many physical models, such as the organic membrane, macromolecule material and even-clump DNA, plasmas physics and so on.

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