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.

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.

MULTI-SOLITON SOLUTIONS AND THEIR INTERACTIONS FOR THE (2+1)-DIMENSIONAL SAWADA-KOTERA MODEL WITH TRUNCATED PAINLEVÉ EXPANSION, HIROTA BILINEAR METHOD AND SYMBOLIC COMPUTATION

2009 ◽  
Vol 23 (25) ◽  
pp. 5003-5015 ◽  
Author(s):  
XING LÜ ◽  
TAO GENG ◽  
CHENG ZHANG ◽  
HONG-WU ZHU ◽  
XIANG-HUA MENG ◽  
...  
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Symbolic Computation ◽  
Bilinear Form ◽  
Soliton Solutions ◽  
Hirota Bilinear Method ◽  
Bilinear Method ◽  
Truncated Painlevé Expansion ◽  
Hirota Bilinear ◽  
Bilinear Equations

In this paper, the (2+1)-dimensional Sawada-Kotera equation is studied by the truncated Painlevé expansion and Hirota bilinear method. Firstly, based on the truncation of the Painlevé series we obtain two distinct transformations which can transform the (2+1)-dimensional Sawada-Kotera equation into two bilinear equations of different forms (which are shown to be equivalent). Then employing Hirota bilinear method, we derive the analytic one-, two- and three-soliton solutions for the bilinear equations via symbolic computation. A formula which denotes the N-soliton solution is given simultaneously. At last, the evolutions and interactions of the multi-soliton solutions are graphically discussed as well. It is worthy to be noted that the truncated Painlevé expansion provides a useful dependent variable transformation which transforms a partial differential equation into its bilinear form and by means of the bilinear form, further study of the original partial differential equation can be conducted.

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.

Two–Soliton Solutions Of The Kadomtsevpetviashvili Equation

2012 ◽  
Author(s):  
Wei King Tiong ◽  
Chee Tiong Ong ◽  
Mukheta Isa
Keyword(s):  
Analytic Solution ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Hirota Bilinear Method ◽  
Kp Equation ◽  
Bilinear Method ◽  
Traditional Group ◽  
Soliton Interactions ◽  
De Vries ◽  
Hirota Bilinear

Beberapa keputusan tentang penjanaan penyelesaian soliton oleh persamaan Kadomtsev–Petviashvili akan dibincangkan dalam kertas ini. Kaedah teori kumpulan mampu memberikan penyelesaian secara analitik kerana persamaan KP mempunyai ketakterhinggaan banyaknya hukum keabadian. Dengan kaedah Bilinear Hirota, ditunjukkan melalui simulasi berkomputer bagaimana penyelesaian dua soliton persamaan KP mampu menghasilkan strukturstruktur “triad”, kuadruplet dan struktur tak beresonan dalam interaksi soliton. Kata kunci: Soliton, kaedah Bilinear Hirota, persamaan Kortewegde Vries dan Kadomtsev- Petviashvili Several findings on soliton solutions generated by the Kadomtsev–Petviashvili (KP) equation were discussed in this paper. This equation is a two dimensional of the Korteweg–de Vries (KdV) equation. Traditional group–theoretical approach can generate analytic solution of solitons because KP equation has infinitely many conservation laws. By using Hirota Bilinear method, we show via computer simulation how two solitons solution of KP equation produces triad, quadruplet and a non–resonance structures in soliton interactions. Key words: Soliton, Hirota Bilinear method, Korteweg-de Vries and Kadomtsev-Petviashvili equations

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.

ANALYTICAL INVESTIGATION OF THE CAUDREY–DODD–GIBBON–KOTERA–SAWADA EQUATION USING SYMBOLIC COMPUTATION

2013 ◽  
Vol 27 (06) ◽  
pp. 1250124 ◽  
Author(s):  
XIAO-GE XU ◽  
XIANG-HUA MENG ◽  
CHUN-YI ZHANG ◽  
YI-TIAN GAO
Keyword(s):  
Symbolic Computation ◽  
Bilinear Form ◽  
Soliton Solutions ◽  
Lax Pair ◽  
Analytical Investigation ◽  
Hirota Bilinear Method ◽  
Bilinear Method ◽  
Nonlinear Superposition ◽  
Hirota Bilinear ◽  
Nonlinear Superposition Formula

In this paper, the Caudrey–Dodd–Gibbon–Kotera–Sawada (CDGKS) equation is analytically investigated using the Hirota bilinear method. Based on the bilinear form of the CDGKS equation, its N-soliton solution in explicit form is derived with the aid of symbolic computation. Besides the soliton solutions, several integrable properties such as the Bäcklund transformation, the Lax pair and the nonlinear superposition formula are also derived for the CDGKS equation.

N-Soliton Solutions for (2+1)-Dimensional Nonlinear Dissipative Zabolotskaya-Khokhlov System

2012 ◽  
Vol 424-425 ◽  
pp. 564-567
Author(s):  
Bang Qing Li ◽  
Cong Wang
Keyword(s):  
Symbolic Computation ◽  
Soliton Solutions ◽  
Evolution Process ◽  
Hirota Bilinear Method ◽  
Bilinear Method ◽  
New Type ◽  
Computation Algorithm ◽  
Hirota Bilinear

Applying a symbolic computation algorithm, namely, the improved Hirota bilinear method, a new type of the N-soliton solutions is obtained for the (2+1)-dimensional nonlinear dissipative Zabolotskaya-Khokhlov system. The solutions can be expressed explicitly. Furthermore, the evolution process is investigated for the N-soliton solutions

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 Lump Solutions, Multi Lump Solutions and More Soliton Solutions of a Novel (2+1)-dimensional Nonlinear Evolution Equation

2021 ◽  
Author(s):  
Hongcai Ma ◽  
Shupan Yue ◽  
Yidan Gao ◽  
Aiping Deng
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
Bilinear Method ◽  
Test Function ◽  
Lump Solutions ◽  
Hirota Bilinear ◽  
Test Function Method

Abstract Exact solutions of a new (2+1)-dimensional nonlinear evolution equation are studied. Through the Hirota bilinear method, the test function method and the improved tanh-coth and tah-cot method, with the assisstance of symbolic operations, one can obtain the lump solutions, multi lump solutions and more soliton solutions. Finally, by determining different parameters, we draw the three-dimensional plots and density plots at different times.

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.

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