New interaction phenomenon and the periodic lump wave for the Jimbo–Miwa equation

2019 ◽  
Vol 33 (06) ◽  
pp. 1950067 ◽  
Author(s):  
Runfa Zhang ◽  
Sudao Bilige
Keyword(s):  
Classical Mechanics ◽  
Three Dimensional ◽  
Bilinear Method ◽  
Interaction Solutions ◽  
Wave Solutions ◽  
Lump Wave ◽  
Physical Features ◽  
The Waves ◽  
Hirota Bilinear ◽  
Interaction Phenomenon

By using the Hirota bilinear method, new interaction solutions and the periodic lump wave solutions for the Jimbo–Miwa equation are successfully solved via symbolic computation with Maple. These new solutions greatly enrich the existing literature on the Jimbo–Miwa equation. Via the three-dimensional images and density images, the physical characteristics of the interactions and the periodic lump wave are well observed. These physical features of the waves obtained in this paper will be widely used in the fields of electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics.

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.

RIEMANN THETA FUNCTIONS SOLUTIONS WITH RATIONAL CHARACTERISTICS FOR (2+1)-DIMENSIONAL SINH-GORDON EQUATION

2010 ◽  
Vol 24 (06) ◽  
pp. 575-584
Author(s):  
YANG FENG ◽  
HONG-QING ZHANG
Keyword(s):  
Gordon Equation ◽  
Theta Functions ◽  
Periodic Wave ◽  
Bilinear Method ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Wave Numbers ◽  
Riemann Theta Functions ◽  
The Waves ◽  
Hirota Bilinear

In this letter, we use the Riemann theta functions with rational characteristics and the Hirota bilinear method to construct quasi-periodic wave solutions for (2+1)-dimensional sinh-Gordon equation. This method not only conveniently obtains quasi-periodic solutions of nonlinear equations, but also directly gets the explicit expressions of frequencies, wave numbers, phase and amplitudes for the waves.

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.

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.

Lump-type and interaction solutions to an extended (3 + 1)-dimensional Jimbo–Miwa equation

2020 ◽  
Vol 34 (07) ◽  
pp. 2050043 ◽  
Author(s):  
Feng-Hua Qi ◽  
Wen-Xiu Ma ◽  
Qi-Xing Qu ◽  
Pan Wang
Keyword(s):  
Rogue Wave ◽  
Bilinear Method ◽  
Interaction Solutions ◽  
Wave Solutions ◽  
Double Exponential ◽  
Dynamical Features ◽  
Wave Phenomena ◽  
Hirota Bilinear ◽  
Double Exponential Function ◽  
Dimensional Wave

By using the Hirota bilinear method, we construct new lump-type solutions to an extended [Formula: see text]-dimensional Jimbo–Miwa equation, which describes certain [Formula: see text]-dimensional wave phenomena in physics. The presented solutions contain 10 arbitrary parameters and only need to satisfy four restrictive conditions to be analytic, thereby enriching the existing lump-type solutions. Moreover, we compute their interaction solutions with double exponential function waves, which include rogue wave solutions. Dynamical features of the obtained solutions are graphically exhibited.

Periodic type and periodic cross-kink wave solutions to the (2 + 1)-dimensional breaking soliton equation arising in fluid dynamics

2019 ◽  
Vol 33 (23) ◽  
pp. 1950277 ◽  
Author(s):  
Onur Alp Ilhan ◽  
Jalil Manafian
Keyword(s):  
Fluid Dynamics ◽  
Classical Mechanics ◽  
Three Dimensional ◽  
Periodic Wave ◽  
Heat Transfer Fluid ◽  
Bilinear Method ◽  
Wave Solutions ◽  
Gas Plasma ◽  
Package Program ◽  
Kink Wave

In this paper, we have acquired the periodic type and cross-kink wave solutions. In this paper, we use the Hirota bilinear method. With the help of the symbolic calculation and applying the used method, we solve the (2[Formula: see text]+[Formula: see text]1)-dimensional Breaking Soliton (BS) equation. We obtain some periodic wave and cross-kink wave that have greatly enriched the existing literature on the BS equation. All solutions have been verified back into its corresponding equation with the aid of the Maple package program via the three-dimensional images and density images with the help of Maple, the physical characteristics of these waves are described very well. These will be widely used to describe many interesting physical phenomena in the fields of gas, plasma, optics, acoustics, heat transfer, fluid dynamics, classical mechanics and so on.

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.

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.

scholarly journals New Types of Doubly Periodic Standing Wave Solutions for the Coupled Higgs Field Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Gui-qiong Xu
Keyword(s):  
Field Equation ◽  
Standing Wave ◽  
Higgs Field ◽  
Jacobi Elliptic Function ◽  
Bilinear Method ◽  
Wave Solutions ◽  
New Type ◽  
Function Expression ◽  
Parameter Values ◽  
Hirota Bilinear

Based on the Hirota bilinear method and theta function identities, we obtain a new type of doubly periodic standing wave solutions for a coupled Higgs field equation. The Jacobi elliptic function expression and long wave limits of the periodic solutions are also presented. By selecting appropriate parameter values, we analyze the interaction properties of periodic-periodic waves and periodic-solitary waves by some figures.

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.

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