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.

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.

Mixed lump-solitons, periodic lump and breather soliton solutions for (2 + 1)-dimensional extended Kadomtsev–Petviashvili dynamical equation

2019 ◽  
Vol 33 (05) ◽  
pp. 1950019 ◽  
Author(s):  
Iftikhar Ahmed ◽  
Aly R. Seadawy ◽  
Dianchen Lu
Keyword(s):  
Symbolic Computation ◽  
Dynamical Equation ◽  
Soliton Solutions ◽  
Hirota Bilinear Method ◽  
Kp Equation ◽  
Bilinear Method ◽  
Lump Solutions ◽  
Contour Plots ◽  
Hirota Bilinear

In this study, based on the Hirota bilinear method, mixed lump-solitons, periodic lump and breather soliton solutions are derived for (2 + 1)-dimensional extended KP equation with the aid of symbolic computation. Furthermore, dynamics of these solutions are explained with 3d plots and 2d contour plots by taking special choices of the involved parameters. Through the mixed lump-soliton solutions, we observe two fusion phenomena, first from interaction of lump and single soliton and other from interaction of lump with two solitons. In both cases, lump moves gradually towards soliton and transfers energy until it completely merges with the solitons. We also observe new characteristics of periodic lump solutions and kinky breather solitons.

A (2+1)-dimensional shallow water equation and its explicit lump solutions

2019 ◽  
Vol 33 (07) ◽  
pp. 1950038 ◽  
Author(s):  
Solomon Manukure ◽  
Yuan Zhou
Keyword(s):  
Shallow Water Equation ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Bilinear Method ◽  
Lump Solutions ◽  
Contour Plots ◽  
Dimensional Equation ◽  
New Equation ◽  
Necessary And Sufficient ◽  
Hirota Bilinear

We introduce a new (2+1)-dimensional equation by modifying the potential form of the Calogero–Bogoyavlenskii–Schiff (CBS) equation. By applying the Hirota bilinear method, we construct explicit lump solutions to this new equation and establish necessary and sufficient conditions that guarantee that the solutions are analytic and rationally localized in all directions in space. We also depict the evolution of the profiles of some selected lump solutions with three-dimensional and contour plots. It is immediately observed that the lump solutions generated are solitary wave type solutions as is the case with the KP equation.

Rational solutions and lump solutions to the (3+1)-dimensional Mel’nikov equation

2019 ◽  
Vol 34 (03) ◽  
pp. 2050033 ◽  
Author(s):  
Xuelin Yong ◽  
Xiaoyu Li ◽  
Yehui Huang ◽  
Wen-Xiu Ma ◽  
Yong Liu
Keyword(s):  
Three Dimensional ◽  
Explicit Representation ◽  
Hirota Bilinear Method ◽  
Matrix Elements ◽  
Rational Solutions ◽  
Bilinear Method ◽  
Lump Solutions ◽  
First Order ◽  
Special Value ◽  
Hirota Bilinear

In this paper, explicit representation of general rational solutions for the (3[Formula: see text]+[Formula: see text]1)-dimensional Mel’nikov equation is derived by employing the Hirota bilinear method. It is obtained in terms of determinants whose matrix elements satisfy some differential and difference relations. By selecting special value of the parameters involved, the first-order and second-order lump solutions are given and their dynamic characteristics are illustrated by two- and three-dimensional figures.

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.

Applications of mixed lump-solitons solutions and multi-peaks solitons for newly extended (2+1)-dimensional Boussinesq wave equation

2019 ◽  
Vol 33 (29) ◽  
pp. 1950363 ◽  
Author(s):  
Dianchen Lu ◽  
Aly R. Seadawy ◽  
Iftikhar Ahmed
Keyword(s):  
Boussinesq Equation ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
Function Technique ◽  
Two Dimensional ◽  
Hirota Bilinear Method ◽  
Bilinear Method ◽  
Contour Plots ◽  
Hirota Bilinear ◽  
Interaction Phenomena

In this work, based on the Hirota bilinear method, mixed lump-solitons solutions and multi-peaks solitons are derived for a new extended (2[Formula: see text]+[Formula: see text]1)-dimensional Boussinesq equation by using ansatz function technique with symbolic computation. Through the mixed lump-solitons, we obtained two types of interaction phenomena, first from lump-single soliton solution and other from lump-two soliton solutions and their dynamics is given by three-dimensional plots and two-dimensional contour plots by taking appropriate values of given parameters. Furthermore, we obtained new patterns of multi-peaks solitons.

scholarly journals A Study on Lump Solutions to a Generalized Hirota-Satsuma-Ito Equation in (2+1)-Dimensions

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Wen-Xiu Ma ◽  
Jie Li ◽  
Chaudry Masood Khalique
Keyword(s):  
Three Dimensional ◽  
Lump Solution ◽  
Lump Solutions ◽  
Solution Structures ◽  
New Class ◽  
Contour Plots ◽  
Bilinear Formulation ◽  
Hirota Bilinear ◽  
Interesting Solution ◽  
Ito Equation

The Hirota-Satsuma-Ito equation in (2+1)-dimensions passes the three-soliton test. This paper aims to generalize this equation to a new one which still has abundant interesting solution structures. Based on the Hirota bilinear formulation, a symbolic computation with a new class of Hirota-Satsuma-Ito type equations involving general second-order derivative terms is conducted to require having lump solutions. Explicit expressions for lump solutions are successfully presented in terms of coefficients in a generalized Hirota-Satsuma-Ito equation. Three-dimensional plots and contour plots of a special presented lump solution are made to shed light on the characteristic of the resulting lump solutions.

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.

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.

Sign in / Sign up

Export Citation Format

Share Document