Localized interaction solution and its dynamics of the extended Hirota–Satsuma–Ito equation

2021 ◽  
pp. 2150313
Author(s):  
Jian-Ping Yu ◽  
Wen-Xiu Ma ◽  
Chaudry Masood Khalique ◽  
Yong-Li Sun
Keyword(s):  
Numerical Simulations ◽  
Rogue Wave ◽  
The Other ◽  
Hirota Bilinear Method ◽  
Bilinear Method ◽  
Interaction Solutions ◽  
Physical Phenomena ◽  
Wave Phenomena ◽  
Hirota Bilinear ◽  
Ito Equation

In this research, we will introduce and study the localized interaction solutions and th eir dynamics of the extended Hirota–Satsuma–Ito equation (HSIe), which plays a key role in studying certain complex physical phenomena. By using the Hirota bilinear method, the lump-type solutions will be firstly constructed, which are almost rationally localized in all spatial directions. Then, three kinds of localized interaction solutions will be obtained, respectively. In order to study the dynamic behaviors, numerical simulations are performed. Two interesting physical phenomena are found: one is the fission and fusion phenomena happening during the procedure of their collisions; the other is the rogue wave phenomena triggered by the interaction between a lump-type wave and a soliton wave.

Lump-type and interaction solutions to an extended (3 + 1)-dimensional Jimbo–Miwa equation

2020 ◽  
Vol 34 (07) ◽  
pp. 2050043 ◽  
Author(s):  
Feng-Hua Qi ◽  
Wen-Xiu Ma ◽  
Qi-Xing Qu ◽  
Pan Wang
Keyword(s):  
Rogue Wave ◽  
Bilinear Method ◽  
Interaction Solutions ◽  
Wave Solutions ◽  
Double Exponential ◽  
Dynamical Features ◽  
Wave Phenomena ◽  
Hirota Bilinear ◽  
Double Exponential Function ◽  
Dimensional Wave

By using the Hirota bilinear method, we construct new lump-type solutions to an extended [Formula: see text]-dimensional Jimbo–Miwa equation, which describes certain [Formula: see text]-dimensional wave phenomena in physics. The presented solutions contain 10 arbitrary parameters and only need to satisfy four restrictive conditions to be analytic, thereby enriching the existing lump-type solutions. Moreover, we compute their interaction solutions with double exponential function waves, which include rogue wave solutions. Dynamical features of the obtained solutions are graphically exhibited.

Lump-type solution, rogue wave, fusion and fission phenomena for the (2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada equation

2019 ◽  
Vol 33 (18) ◽  
pp. 1950198 ◽  
Author(s):  
Tao Fang ◽  
Chun-Na Gao ◽  
Hui Wang ◽  
Yun-Hu Wang
Keyword(s):  
Polynomial Function ◽  
Rogue Wave ◽  
Quadratic Polynomial ◽  
Hirota Bilinear Method ◽  
Type Solution ◽  
Bilinear Method ◽  
Interaction Solutions ◽  
Hirota Bilinear ◽  
Bilinear Equation

By means of the Hirota bilinear method, lump-type solution and two types of interaction solutions of the (2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada equation are obtained, respectively. Lump-type solution is constructed by assuming f in the corresponding bilinear equation as a ternary quadratic polynomial function. It is interesting that the rogue wave is aroused by the interaction between one-lump soliton and a pair of stripe solitons, and the fusion and fission phenomena are also found in the interaction between lump solitons and one-stripe soliton. The corresponding phenomena are vividly demonstrated by the graphs.

Novel characteristics of lump and lump–soliton interaction solutions to the (2+1)-dimensional Alice–Bob Hirota–Satsuma–Ito equation

2020 ◽  
Vol 34 (36) ◽  
pp. 2050419
Author(s):  
Wang Shen ◽  
Zhengyi Ma ◽  
Jinxi Fei ◽  
Quanyong Zhu
Keyword(s):  
Exact Solutions ◽  
Symbolic Computation ◽  
Three Dimensional ◽  
Soliton Interaction ◽  
Hirota Bilinear Method ◽  
Bilinear Method ◽  
Interaction Solutions ◽  
Hirota Bilinear ◽  
Ito Equation

Based on the Hirota bilinear method and symbolic computation, abundant exact solutions, including lump, lump–soliton, and breather solutions, are computed for the coupled Alice–Bob system of the Hirota–Satsuma–Ito equation in (2 + 1)-dimensions. The three-dimensional figures of these solutions are presented, which illustrate the characteristics of these solutions.

Lump solutions to a generalized Kadomtsev–Petviashvili–Ito equation

2021 ◽  
pp. 2150437
Author(s):  
Liyuan Ding ◽  
Wen-Xiu Ma ◽  
Yehui Huang
Keyword(s):  
Symbolic Computation ◽  
Three Dimensional ◽  
Order Derivative ◽  
Hirota Bilinear Method ◽  
Bilinear Method ◽  
Lump Solutions ◽  
Dynamical Behaviors ◽  
Contour Plots ◽  
Hirota Bilinear ◽  
Ito Equation

A (2+1)-dimensional generalized Kadomtsev–Petviashvili–Ito equation is introduced. Upon adding some second-order derivative terms, its various lump solutions are explicitly constructed by utilizing the Hirota bilinear method and calculated through the symbolic computation system Maple. Furthermore, two specific lump solutions are obtained with particular choices of the parameters and their dynamical behaviors are analyzed through three-dimensional plots and contour plots.

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.

Y-shaped soliton solutions for the (2+1)-dimensional bidirectional Sawada–Kotera equation

2021 ◽  
Author(s):  
Shuxin Yang ◽  
Zhao Zhang ◽  
Biao Li
Keyword(s):  
Soliton Solutions ◽  
Complex Interaction ◽  
High Order ◽  
Hirota Bilinear Method ◽  
Bilinear Method ◽  
Dynamic Behaviors ◽  
Interaction Solutions ◽  
Localized Waves ◽  
Hirota Bilinear ◽  
Interaction Phenomenon

On the basis of the Hirota bilinear method, resonance Y-shaped soliton and its interaction with other localized waves of (2+1)-dimensional bidirectional Sawada–Kotera equation are derived by introducing the constraint conditions. These types of mixed soliton solutions exhibit complex interaction phenomenon between the resonance Y-shaped solitons and line waves, breather waves, and high-order lump waves. The dynamic behaviors of the interaction solutions are analyzed and illustrated.

Lump and interaction solutions of nonlinear partial differential equations

2019 ◽  
Vol 33 (11) ◽  
pp. 1950133 ◽  
Author(s):  
Yong-Li Sun ◽  
Wen-Xiu Ma ◽  
Jian-Ping Yu ◽  
Bo Ren ◽  
Chaudry Masood Khaliqu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Hirota Bilinear Method ◽  
Kp Equation ◽  
Bilinear Method ◽  
Partial Differential ◽  
Interaction Solutions ◽  
Kink Waves ◽  
Hirota Bilinear

In this paper, lump solutions of nonlinear partial differential equations, the generalized (2[Formula: see text]+[Formula: see text]1)-dimensional KP equation and the Jimbo–Miwa equation, are studied by using the Hirota bilinear method and carrying out symbolic computations in Maple. Moreover, the interaction solutions, i.e. collisions between lump waves and kink waves, are investigated. A group of graphs are plotted to illustrate the dynamics of the obtained results.

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 Abundant lump solutions and interaction solutions of a (3+1)-D Kadomtsev-Petviashvili equation

2019 ◽  
Vol 23 (4) ◽  
pp. 2437-2445 ◽  
Author(s):  
Xiaoqing Gao ◽  
Sudao Bilige ◽  
Jianqing Lü ◽  
Yuexing Bai ◽  
Runfa Zhang ◽  
...  
Keyword(s):  
Lump Solution ◽  
Solution Properties ◽  
Hirota Bilinear Method ◽  
Bilinear Method ◽  
Lump Solutions ◽  
Interaction Solutions ◽  
Petviashvili Equation ◽  
Contour Plots ◽  
Hirota Bilinear

In this paper, abundant lump solutions and two types of interaction solutions of the (3+1)-D Kadomtsev-Petviashvili equation are obtained by the Hirota bilinear method. Some contour plots with different determinant values are sequentially given to show that the corresponding lump solution tends to zero when the deter-minant approaches to zero. The interaction solutions with special parameters are plotted to elucidate the solution properties.

scholarly journals Abundant Lump-Type Solutions and Interaction Solutions for a Nonlinear (3+1) Dimensional Model

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
R. Sadat ◽  
M. Kassem ◽  
Wen-Xiu Ma
Keyword(s):  
Three Dimensional ◽  
Higher Dimensions ◽  
Hirota Bilinear Method ◽  
Dimensional Model ◽  
Bilinear Method ◽  
Interaction Solutions ◽  
Special Cases ◽  
Contour Plots ◽  
Dynamical Features ◽  
Hirota Bilinear

We explore dynamical features of lump solutions as diversion and propagation in the space. Through the Hirota bilinear method and the Cole-Hopf transformation, lump-type solutions and their interaction solutions with one- or two-stripe solutions have been generated for a generalized (3+1) shallow water-like (SWL) equation, via symbolic computations associated with three different ansatzes. The analyticity and localization of the resulting solutions in the (x,y,z, and t) space have been analyzed. Three-dimensional plots and contour plots are made for some special cases of the solutions to illustrate physical motions and peak dynamics of lump soliton waves in higher dimensions. The study of lump-type solutions moderates the visuality of optics media and oceanography waves.

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