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.

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.

Lump-type, breather and interaction solutions to the (3+1)-dimensional generalized KdV-type equation

2020 ◽  
Vol 34 (29) ◽  
pp. 2050329
Author(s):  
Pengfei Han ◽  
Taogetusang
Keyword(s):  
Free Choice ◽  
Three Dimensional ◽  
Type Equation ◽  
Type Model ◽  
Physical Explanation ◽  
Bilinear Method ◽  
Interaction Solutions ◽  
Contour Plots ◽  
Dimensional Soliton ◽  
Hirota Bilinear

The [Formula: see text]-dimensional generalized Korteweg-de Vries (KdV)-type model equation is investigated based on the Hirota bilinear method. Diversity of exact solutions for this equation are obtained with the help of symbolic computation. We depicted the physical explanation of the extracted solutions with the free choice of the different parameters by plotting three-dimensional plots and contour plots. The obtained results are useful in gaining the understanding of high dimensional soliton-like structures equation related to mathematical physics branches, natural sciences and engineering areas.

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.

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.

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.

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.

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.

scholarly journals Mixed Rational-Exponential Solutions to the Kadomtsev-Petviashvili-II Equation with a Self-Consistent Source

2020 ◽  
Vol 2020 ◽  
pp. 1-5
Author(s):  
Dan Su ◽  
Wen-Xiu Ma ◽  
Xuelin Yong ◽  
Yehui Huang
Keyword(s):  
Three Dimensional ◽  
Typical Feature ◽  
Time Variable ◽  
Hirota Bilinear Method ◽  
Bilinear Method ◽  
Hybrid Type ◽  
Self Consistent ◽  
Hirota Bilinear

Explicit rational-exponential solutions for the Kadomtsev-Petviashvili-II equation with a self-consistent source (KPIIESCS) are studied by the Hirota bilinear method. One typical feature for this hybrid type of solutions is that they contain two arbitrary functions of time variable t which affect the amplitudes and propagation trajectories. The dynamics of solutions are demonstrated by the three-dimensional figures. The method used here is quite general and can be applied to other equations with self-content sources.

Interaction phenomenon to dimensionally reducedp-gBKP equation

2018 ◽  
Vol 32 (06) ◽  
pp. 1850074 ◽  
Author(s):  
Runfa Zhang ◽  
Sudao Bilige ◽  
Yuexing Bai ◽  
Jianqing Lü ◽  
Xiaoqing Gao
Keyword(s):  
Three Dimensional ◽  
Quadratic Function ◽  
Cosine Function ◽  
Interaction Solutions ◽  
Hyperbolic Cosine ◽  
Hirota Bilinear Form ◽  
Dynamical Features ◽  
Hyperbolic Cosine Function ◽  
Hirota Bilinear ◽  
Interaction Phenomenon

Based on searching the combining of quadratic function and exponential (or hyperbolic cosine) function from the Hirota bilinear form of the dimensionally reduced p-gBKP equation, eight class of interaction solutions are derived via symbolic computation with Mathematica. The submergence phenomenon, presented to illustrate the dynamical features concerning these obtained solutions, is observed by three-dimensional plots and density plots with particular choices of the involved parameters between the exponential (or hyperbolic cosine) function and the quadratic function. It is proved that the interference between the two solitary waves is inelastic.

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