General M-lump, high-order breather, and localized interaction solutions to (2 + 1)-dimensional generalized Bogoyavlensky-Konopelchenko equation

2021 ◽  
Author(s):  
Hongcai Ma ◽  
Yunxiang Bai ◽  
Aiping Deng
Keyword(s):  
High Order ◽  
Interaction Solutions

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.

Dynamical analysis of solitary waves, lumps and interaction phenomena of a (2+1)-dimensional high-order nonlinear evolution equation

2019 ◽  
Vol 33 (16) ◽  
pp. 1950181 ◽  
Author(s):  
Bo Ren ◽  
Zhi-Mei Lou ◽  
Yong-Li Sun ◽  
Zhi-Wei He
Keyword(s):  
Solitary Waves ◽  
Bilinear Form ◽  
Nonlinear Evolution ◽  
Quadratic Function ◽  
High Order ◽  
Dynamical Analysis ◽  
Interaction Solutions ◽  
Variable Function ◽  
Hirota Bilinear Form ◽  
Hirota Bilinear

A (2[Formula: see text]+[Formula: see text]1)-dimensional high-order nonlinear evolution (HNE) equation is considered in this paper. A Hirota bilinear form of the HNE equation is constructed by the dependent variable function. Solitary waves are derived by solving the Hirota bilinear form of the HNE equation. Lump waves of the HNE equation are obtained by introducing a positive quadratic function. By mixing an exponential function or two exponential functions with a quadratic function, interaction solutions between a lump and a one-soliton, and between a lump and a two-soliton are presented. For the interaction solution between a lump and a two-soliton, this kind of solution can be considered as a special rogue wave. The propagation phenomena of these explicit solutions are illustrated by some graphs.

scholarly journals Rational Solutions and Their Interaction Solutions of the (3+1)-Dimensional Jimbo-Miwa Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-18 ◽  
Author(s):  
Xiaomin Wang ◽  
Sudao Bilige ◽  
Jing Pang
Keyword(s):  
Nonlinear Evolution ◽  
Rational Solution ◽  
Three Dimensional ◽  
High Order ◽  
Lump Solution ◽  
Rational Solutions ◽  
Bilinear Method ◽  
Interaction Solution ◽  
Interaction Solutions ◽  
Contour Plots

In this paper, we gave a form of rational solution and their interaction solution to a nonlinear evolution equation. The rational solution contained lump solution, general lump solution, high-order lump solution, lump-type solution, etc. Their interaction solution contained the classical interaction solution, such as the lump-kink solution and the lump-soliton solution. As the example, by using the generalized bilinear method and symbolic computation Maple, we obtained abundant high-order lump-type solutions and their interaction solutions between lumps and other function solutions under certain constraints of the (3+1)-dimensional Jimbo-Miwa equation. Via three-dimensional plots, contour plots and density plots with the help of Maple, the physical characteristics and structures of these waves are described very well. These solutions have greatly enriched the exact solutions of the (3+1)-dimensional Jimbo-Miwa equation on the existing literature.

Multiple breathers and high-order rational solutions of the (3+1)-dimensional B-type Kadomtsev–Petviashvili equation

2021 ◽  
Author(s):  
Na Liu ◽  
Xinhua Tang ◽  
Weiwei Zhang
Keyword(s):  
Soliton Solutions ◽  
High Order ◽  
Rational Solutions ◽  
Bilinear Method ◽  
Dynamical Characteristics ◽  
Interaction Solutions ◽  
Petviashvili Equation ◽  
Wave Limit ◽  
Hirota Bilinear ◽  
Bkp Equation

This paper is devoted to obtaining the multi-soliton solutions, high-order breather solutions and high-order rational solutions of the (3+1)-dimensional B-type Kadomtsev–Petviashvili (BKP) equation by applying the Hirota bilinear method and the long-wave limit approach. Moreover, the interaction solutions are constructed by choosing appropriate value of parameters, which consist of four waves for lumps, breathers, rouges and solitons. Some dynamical characteristics for the obtained exact solutions are illustrated using figures.

High order nonlocal symmetries and exact interaction solutions of the variable coefficient KdV equation

2019 ◽  
Vol 88 ◽  
pp. 132-140 ◽  
Author(s):  
Xiangpeng Xin ◽  
Hanze Liu ◽  
Linlin Zhang ◽  
Zenggui Wang
Keyword(s):  
Variable Coefficient ◽  
Kdv Equation ◽  
High Order ◽  
Nonlocal Symmetries ◽  
Interaction Solutions

scholarly journals The High Order Interaction Solutions Comprising Lump Solitons for the (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada Equation

2020 ◽  
Author(s):  
Jian Hong Zhuang ◽  
Yaqing Liu ◽  
Juan Juan Wu ◽  
Ping Zhuang ◽  
Xin Chen ◽  
...  
Keyword(s):  
High Order ◽  
High Order Interaction ◽  
Order Interaction ◽  
Interaction Solutions

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.

scholarly journals Soliton molecules and abundant interaction solutions of a general high-order Burgers equation

2021 ◽  
pp. 104052
Author(s):  
Gaizhu Qu ◽  
Xiaorui Hu ◽  
Zhengwu Miao ◽  
Shoufeng Shen ◽  
Mengmeng Wang
Keyword(s):  
Burgers Equation ◽  
High Order ◽  
Interaction Solutions
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