scholarly journals Localized interaction solutions of the (2+1)-dimensional Ito Equation

2021 ◽  
Author(s):  
Hongcai Ma ◽  
Hanfang Wu ◽  
Wenxiu Ma ◽  
Aiping Deng
Keyword(s):  
Exact Solutions ◽  
Energy Distributions ◽  
Bilinear Transformation ◽  
Interaction Solutions ◽  
Higher Dimensional ◽  
Dynamical Properties ◽  
Free Parameters ◽  
Hirota Bilinear ◽  
Ito Equation

Abstract Localized interaction solutions of the (2+1)-dimensional Ito equation with free parameters are obtained by using a Hirota bilinear transformation. Various plots with particular choices of the involved parameters are made to show energy distributions and dynamical properties of the special exact solutions. This phenomenon may provide us with interesting information on dynamics in the higher-dimensional nonlinear world.

scholarly journals New Soliton Solutions for the Higher-Dimensional Non-Local Ito Equation

2021 ◽  
Vol 10 (1) ◽  
pp. 374-384
Author(s):  
Mustafa Inc ◽  
E. A. Az-Zo’bi ◽  
Adil Jhangeer ◽  
Hadi Rezazadeh ◽  
Muhammad Nasir Ali ◽  
...  
Keyword(s):  
Exact Solutions ◽  
Solution Process ◽  
Soliton Solutions ◽  
Analytic Solutions ◽  
Bright Solitons ◽  
Exact Analytic Solutions ◽  
Higher Dimensional ◽  
Non Local ◽  
Free Parameters ◽  
Ito Equation

Abstract In this article, (2+1)-dimensional Ito equation that models waves motion on shallow water surfaces is analyzed for exact analytic solutions. Two reliable techniques involving the simplest equation and modified simplest equation algorithms are utilized to find exact solutions of the considered equation involving bright solitons, singular periodic solitons, and singular bright solitons. These solutions are also described graphically while taking suitable values of free parameters. The applied algorithms are effective and convenient in handling the solution process for Ito equation that appears in many phenomena.

Interaction solutions for the (2+1)-dimensional Ito equation

2019 ◽  
Vol 33 (13) ◽  
pp. 1950167 ◽  
Author(s):  
Yaning Tang ◽  
Jinli Ma ◽  
Wenxian Xie ◽  
Lijun Zhang
Keyword(s):  
Periodic Function ◽  
Rational Function ◽  
Bilinear Form ◽  
Hyperbolic Function ◽  
Interaction Solution ◽  
Interaction Solutions ◽  
Hirota Bilinear Form ◽  
Dynamical Properties ◽  
Hirota Bilinear ◽  
Ito Equation

In this paper, two classes of interaction solutions of the (2[Formula: see text]+[Formula: see text]1)-dimensional Ito equation are studied in the case of Hirota bilinear form. As the results, the interaction solutions between the rational function and a periodic function as well as the interaction solution between the hyperbolic function and a periodic function are obtained. Based on the interaction solutions, a new transformation is proposed to analyze and discuss the influence of parameters. Furthermore, two kinds of lump solutions can be obtained via the limit behavior of the interaction solutions and the dynamical properties of these solutions are also illustrated.

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.

Some Interaction Solutions of a Reduced Generalised (3+1)-Dimensional Shallow Water Wave Equation for Lump Solutions and a Pair of Resonance Solitons

2017 ◽  
Vol 72 (5) ◽  
pp. 419-424 ◽  
Author(s):  
Yao Wang ◽  
Mei-Dan Chen ◽  
Xian Li ◽  
Biao Li
Keyword(s):  
Shallow Water ◽  
Water Wave ◽  
Dynamic Properties ◽  
Quadratic Function ◽  
Translation Invariance ◽  
Bilinear Transformation ◽  
Lump Solutions ◽  
Interaction Solutions ◽  
Shallow Water Wave ◽  
Hirota Bilinear

AbstractThrough Hirota bilinear transformation and symbolic computation with Maple, a class of lump solutions, rationally localised in all directions in the space, to a reduced generalised (3+1)-dimensional shallow water wave (SWW) equation are prensented. The resulting lump solutions all contain six parameters, two of which are free due to the translation invariance of the SWW equation and the other four of which must satisfy a nonzero determinant condition guaranteeing analyticity and rational localisation of the solutions. Then we derived the interaction solutions for lump solutions and one stripe soliton and the result shows that the particular lump solutions with specific values of the involved parameters will be drowned or swallowed by the stripe soliton. Furthermore, we extend this method to a more general combination of positive quadratic function and hyperbolic functions. Especially, it is interesting that a rogue wave is found to be aroused by the interaction between lump solutions and a pair of resonance stripe solitons. By choosing the values of the parameters, the dynamic properties of lump solutions, interaction solutions for lump solutions and one stripe soliton and interaction solutions for lump solutions and a pair of resonance solitons, are shown by dynamic graphs.

Construction of lump-type and interaction solutions to an extended (3+1)-dimensional Jimbo–Miwa-like equation

2020 ◽  
Vol 34 (13) ◽  
pp. 2050130
Author(s):  
Feng-Hua Qi ◽  
Wen-Xiu Ma ◽  
Pan Wang ◽  
Qi-Xing Qu
Keyword(s):  
Wave Equations ◽  
Periodic Wave ◽  
Dynamical Theory ◽  
Periodic Waves ◽  
Bilinear Method ◽  
Interaction Solutions ◽  
Higher Dimensional ◽  
Kink Waves ◽  
Hirota Bilinear ◽  
Nonlinear Dispersive Wave

We present lump-type solutions and interaction solutions to an extended (3[Formula: see text]+[Formula: see text]1)-dimensional Jimbo–Miwa-like equation. Three classes of lump-type solutions are obtained by the Hirota bilinear method. Interaction solutions are among lump-type solutions, two kink waves and periodic waves, and between two kink waves and a periodic wave are computed. Dynamical characters of the obtained solutions are graphically exhibited. These wave solutions enrich the dynamical theory of higher-dimensional nonlinear dispersive wave equations.

scholarly journals Lump Solutions and Resonance Stripe Solitons to the (2+1)-Dimensional Sawada-Kotera Equation

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Xian Li ◽  
Yao Wang ◽  
Meidan Chen ◽  
Biao Li
Keyword(s):  
Symbolic Computation ◽  
Exponential Function ◽  
Bilinear Form ◽  
Quadratic Function ◽  
Hyperbolic Function ◽  
Lump Solutions ◽  
Interaction Solutions ◽  
Hirota Bilinear Form ◽  
Dynamical Properties ◽  
Hirota Bilinear

Based on the symbolic computation, a class of lump solutions to the (2+1)-dimensional Sawada-Kotera (2DSK) equation is obtained through making use of its Hirota bilinear form and one positive quadratic function. These solutions contain six parameters, four of which satisfy two determinant conditions to guarantee the analyticity and rational localization of the solutions, while the others are free. Then by adding an exponential function into the original positive quadratic function, the interaction solutions between lump solutions and one stripe soliton are derived. Furthermore, by extending this method to a general combination of positive quadratic function and hyperbolic function, the interaction solutions between lump solutions and a pair of resonance stripe solitons are provided. Some figures are given to demonstrate the dynamical properties of the lump solutions, interaction solutions between lump solutions, and stripe solitons by choosing some special parameters.

A variety of wave amplitudes for the conformable fractional (2 + 1)-dimensional Ito equation

2021 ◽  
pp. 2150254
Author(s):  
Emad A. Az-Zo’bi ◽  
Wael A. Alzoubi ◽  
Lanre Akinyemi ◽  
Mehmet Şenol ◽  
Basem S. Masaedeh
Keyword(s):  
Mapping Method ◽  
Jacobi Elliptic Function ◽  
Conformable Derivative ◽  
Hyperbolic Functions ◽  
Fractional Complex Transform ◽  
New Exact Solutions ◽  
Higher Dimensional ◽  
Fractional Orders ◽  
Ito Equation ◽  
Ordinary Derivative

The conformable derivative and adequate fractional complex transform are implemented to discuss the fractional higher-dimensional Ito equation analytically. The Jacobi elliptic function method and Riccati equation mapping method are successfully used for this purpose. New exact solutions in terms of linear, rational, periodic and hyperbolic functions for the wave amplitude are derived. The obtained solutions are entirely new and can be considered as a generalization of the existing results in the ordinary derivative case. Numerical simulations of some obtained solutions with special choices of free constants and various fractional orders are displayed.

N-soliton solutions and localized wave interaction solutions of a (3 + 1)-dimensional potential-Yu–Toda–Sasa–Fukuyamaf equation

2021 ◽  
pp. 2150277
Author(s):  
Hongcai Ma ◽  
Qiaoxin Cheng ◽  
Aiping Deng
Keyword(s):  
Dynamic Behavior ◽  
Soliton Solution ◽  
Soliton Solutions ◽  
Wave Interaction ◽  
Bilinear Transformation ◽  
Interaction Solution ◽  
Interaction Solutions ◽  
Ytsf Equation ◽  
Line Soliton

[Formula: see text]-soliton solutions are derived for a (3 + 1)-dimensional potential-Yu–Toda–Sasa–Fukuyama (YTSF) equation by using bilinear transformation. Some local waves such as period soliton, line soliton, lump soliton and their interaction are constructed by selecting specific parameters on the multi-soliton solutions. By selecting special constraints on the two soliton solutions, period and lump soliton solution can be obtained; three solitons can reduce to the interaction solution between period soliton and line soliton or lump soliton and line soliton under special parameters; the interaction solution among period soliton and two line solitons, or the interaction solution for two period solitons or two lump solitons via taking specific constraints from four soliton solutions. Finally, some images of the results are drawn, and their dynamic behavior is analyzed.

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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