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.

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.

Abundant Lump Solution and Interaction Phenomenon of (3+1)-Dimensional Generalized Kadomtsev–Petviashvili Equation

2019 ◽  
Vol 20 (1) ◽  
pp. 33-40 ◽  
Author(s):  
Jianqing Lü ◽  
Sudao Bilige ◽  
Xiaoqing Gao
Keyword(s):  
Symbolic Computation ◽  
Bilinear Form ◽  
Lump Solution ◽  
Lump Solutions ◽  
Interaction Solution ◽  
Interaction Solutions ◽  
Petviashvili Equation ◽  
Contour Plots ◽  
Special Case ◽  
Interaction Phenomenon

AbstractIn this paper, with the help of symbolic computation system Mathematica, six kinds of lump solutions and two classes of interaction solutions are discussed to the (3+1)-dimensional generalized Kadomtsev–Petviashvili equation via using generalized bilinear form with a dependent variable transformation. Particularly, one special case are plotted as illustrative examples, and some contour plots with different determinant values are presented. Simultaneously, we studied the trajectory of the interaction solution.

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.

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-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.

High-order breathers and semi-rational solutions of the (2+1)-dimensional Yu–Toda–Sasa–Fukuyama equation

2021 ◽  
pp. 2150422
Author(s):  
Mengqi Zheng ◽  
Maohua Li
Keyword(s):  
Time Evolution ◽  
High Order ◽  
Lump Solution ◽  
Hirota Bilinear Method ◽  
Rational Solutions ◽  
Bilinear Method ◽  
Interaction Solutions ◽  
Long Wave ◽  
Wave Limit ◽  
Hirota Bilinear

In this paper, based on the Hirota bilinear method, the high-order breathers and interaction solutions between solitons and breathers of the (2+1)-dimensional Yu–Toda–Sasa–Fukuyama equation are investigated. The lump and semi-rational solutions are obtained by applying the long wave limit of the [Formula: see text]-soliton solution. Two types of semi-rational solutions are derived by choosing specific parameters, which are the mixture of the lump solution and solitons, and the mixture of the lump solution and breathers. Furthermore, the time evolution diagram illustrate the dynamic behavior 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.

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.

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.

Solitary wave solutions, lump solutions and interactional solutions to the (3 + 1)-dimensional generalized B-type Kadomtsev-Petviashvili equation

2020 ◽  
Vol 34 (07) ◽  
pp. 2050053
Author(s):  
Min Gao ◽  
Hai-Qiang Zhang
Keyword(s):  
Solitary Wave ◽  
Solitary Wave Solution ◽  
Lump Solution ◽  
Solitary Wave Solutions ◽  
Bilinear Method ◽  
Long Wave ◽  
Petviashvili Equation ◽  
Dimensional Equation ◽  
Hirota Bilinear ◽  
Bkp Equation

In this paper, we investigate a [Formula: see text]-dimensional B-type Kadomtsev-Petviashvili (BKP) equation, which is a generalization of the [Formula: see text]-dimensional equation. Based on the Hirota bilinear method and the limit technique of long wave, we systematically construct a family of exact solutions of BKP equation including the [Formula: see text]-solitary wave solution, lump solution as well as interaction solution between lump waves and solitary waves.

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