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.

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.

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 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.

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.

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.

Soliton molecules and some novel hybrid solutions for (3+1)-dimensional B-type Kadomtsev–Petviashvili equation

2021 ◽  
pp. 2150388
Author(s):  
Hongcai Ma ◽  
Huaiyu Huang ◽  
Aiping Deng
Keyword(s):  
Soliton Solutions ◽  
Dynamic Graphs ◽  
Bilinear Method ◽  
Resonance Mechanism ◽  
Long Wave ◽  
Petviashvili Equation ◽  
Hybrid Solutions ◽  
Wave Limit ◽  
Bkp Equation

In recent years, soliton molecules have received reinvigorating scientific interests in physics and other fields. Soliton molecules have been successfully found in optical experiments. In this paper, we attribute the solutions of the (3+1)-dimensional B-type Kadomtsev–Petviashvili (BKP) equation by employing the bilinear method. Based on the [Formula: see text]-soliton solutions, we establish the soliton molecules, asymmetric solitons and some novel hybrid solutions of this equation by means of the velocity resonance mechanism and the long wave limit method. Finally, we give dynamic graphs of soliton molecules, asymmetric solitons and some novel hybrid solutions.

scholarly journals Soliton Molecules and Some Novel Types of Hybrid Solutions to (2 + 1)-Dimensional Variable-Coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Shuxin Yang ◽  
Zhao Zhang ◽  
Biao Li
Keyword(s):  
Variable Coefficient ◽  
Resonance Condition ◽  
Soliton Solutions ◽  
Wave Number ◽  
Long Wave ◽  
Hybrid Solutions ◽  
Wave Limit ◽  
Dimensional Variable

Soliton molecules of the (2 + 1)-dimensional variable-coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada equation are derived by N-soliton solutions and a new velocity resonance condition. Moreover, soliton molecules can become asymmetric solitons when the distance between two solitons of the molecule is small enough. Finally, we obtained some novel types of hybrid solutions which are components of soliton molecules, lump waves, and breather waves by applying velocity resonance, module resonance of wave number, and long wave limit method. Some figures are presented to demonstrate clearly dynamics features of these solutions.

High-order breathers, lumps and hybrid solutions to the (2+1)-dimensional fifth-order KdV equation

2019 ◽  
Vol 33 (22) ◽  
pp. 1950255 ◽  
Author(s):  
Wen-Tao Li ◽  
Zhao Zhang ◽  
Xiang-Yu Yang ◽  
Biao Li
Keyword(s):  
Kdv Equation ◽  
Perturbation Expansion ◽  
Soliton Solutions ◽  
High Order ◽  
Bilinear Method ◽  
Long Wave ◽  
Hybrid Solutions ◽  
Wave Limit ◽  
Fifth Order ◽  
Parameter Constraints

In this paper, the (2+1)-dimensional fifth-order KdV equation is analytically investigated. By using Hirota’s bilinear method combined with perturbation expansion, the high-order breather solutions of the fifth-order KdV equation are generated. Then, the high-order lump solutions are also derived from the soliton solutions by a long-wave limit method and some suitable parameter constraints. Furthermore, we extend this method to obtain hybrid solutions by taking long-wave limit for partial soliton solutions. Finally, the dynamic behavior of these solutions is presented in the figures.

Soliton molecules, asymmetric soliton and some novel hybrid solutions for the isospectral BKP equation

2021 ◽  
pp. 2150174
Author(s):  
Hongcai Ma ◽  
Qiaoxin Cheng ◽  
Aiping Deng
Keyword(s):  
Behavior Analysis ◽  
Dynamic Behavior ◽  
Resonance Condition ◽  
Long Wave ◽  
Hybrid Solutions ◽  
Wave Limit ◽  
Bkp Equation

In this paper, we investigate the soliton molecules, asymmetric soliton and some novel hybrid solutions for the isospectral B-type Kadomtsev–Petviashvili (BKP) equation based on a new resonance condition. The soliton molecules and asymmetric soliton of the isospectral BKP equation can be obtained by selecting the appropriate parameters. Based on velocity resonance, module resonance and long-wave limit method, we can obtain the interactions of soliton molecules, breather waves and lump waves. Finally, we give the graphic of soliton molecules, asymmetric soliton and some novel hybrid solutions, and give the dynamic behavior analysis.

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.

Sign in / Sign up

Export Citation Format

Share Document