Lump, rogue wave, multi-waves and Homoclinic breather solutions for (2+1)-Modified Veronese Web equation

2021 ◽  
Vol 35 (04) ◽  
pp. 2150055
Author(s):  
S. T. R. Rizvi ◽  
Aly R. Seadawy ◽  
S. Ahmed ◽  
M. Younis ◽  
K. Ali
Keyword(s):  
Rogue Wave ◽  
Nonlinear Partial Differential Equation ◽  
Quadratic Function ◽  
Wave Transformation ◽  
Physical Parameters ◽  
Wave Solutions ◽  
Hirota Bilinear Form ◽  
Wave Phenomena ◽  
Hirota Bilinear ◽  
Linearly Degenerate

This work addresses the four main inducements: Lump, rogue wave, Homoclinic breather and multi-wave solutions for (2+1)-Modified Veronese Web (MVW) equation via Hirota bilinear approach and the ansatz technique. This model is a linearly degenerate integrable nonlinear partial differential equation (NLPDE) and can also be used to admit a differential covering with nonremoval physical parameters. By assuming the function [Formula: see text] in the Hirota bilinear form of the presented model as the general quadratic function, trigonometric function and exponential function form, also with appropriate set of parameters, we have prevented the lump, rogue wave, breather and multi-wave solutions successfully. A precise compatible wave transformation is utilized to obtain multi-wave solutions of governing model. Also, the motion track of the lump, Rogue wave and multi-waves is also explained both physically and theoretically. These new results contain some special arbitrary constants that can be useful to spell out diversity in qualitative features of wave phenomena.

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.

scholarly journals Lump, lump-one stripe, multiwave and breather solutions for the Hunter–Saxton equation

Open Physics ◽  
2021 ◽  
Vol 19 (1) ◽  
pp. 1-10
Author(s):  
Aly R. Seadawy ◽  
Syed Tahir Raza Rizvi ◽  
Sarfraz Ahmad ◽  
Muhammad Younis ◽  
Dumitru Baleanu
Keyword(s):  
Liquid Crystal ◽  
Bilinear Form ◽  
Three Dimensional ◽  
Quadratic Function ◽  
Trigonometric Function ◽  
Director Field ◽  
Wave Dynamics ◽  
Hirota Bilinear Form ◽  
Wave Phenomena ◽  
Hirota Bilinear

Abstract The aim of this article was to address the lump, lump-one stripe, multiwave and breather solutions for the Hunter–Saxton equation with the aid of Hirota bilinear technique. This model concerns in a massive nematic liquid crystal director field. By choosing the function f in Hirota bilinear form, as the general quadratic function, trigonometric function and exponential function along with appropriate set of parameters, we find the lump, lump-one stripe, multiwave and breather solutions successfully. We also interpreted some three-dimensional and contour profiles to anticipate the wave dynamics. These newly obtained solutions have some arbitrary constants and so can be applicable to explain diversity in qualitative features of wave phenomena.

Abundant rogue wave solutions for the (2 + 1)-dimensional generalized Korteweg–de Vries equation

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Huanhuan Lu ◽  
Yufeng Zhang
Keyword(s):  
Vries Equation ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Third Order ◽  
First Order ◽  
Wave Solutions ◽  
De Vries ◽  
Rogue Wave Solutions ◽  
Bilinear Formulation ◽  
Hirota Bilinear

AbstractIn this paper, we analyse two types of rogue wave solutions generated from two improved ansatzs, to the (2 + 1)-dimensional generalized Korteweg–de Vries equation. With symbolic computation, the first-order rogue waves, second-order rogue waves, third-order rogue waves are generated directly from the first ansatz. Based on the Hirota bilinear formulation, another type of one-rogue waves and two-rogue waves can be obtained from the second ansatz. In addition, the dynamic behaviours of obtained rogue wave solutions are illustrated graphically.

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.

Lump-type solutions, interaction solutions and periodic wave solutions of a (3+1)-dimensional Korteweg–de Vries equation

2019 ◽  
Vol 33 (27) ◽  
pp. 1950319 ◽  
Author(s):  
Hongfei Tian ◽  
Jinting Ha ◽  
Huiqun Zhang
Keyword(s):  
Vries Equation ◽  
Kdv Equation ◽  
Periodic Wave ◽  
Periodic Wave Solutions ◽  
Interaction Solutions ◽  
Dynamical Behaviors ◽  
Wave Solutions ◽  
Hirota Bilinear Form ◽  
De Vries ◽  
Hirota Bilinear

Based on the Hirota bilinear form, lump-type solutions, interaction solutions and periodic wave solutions of a (3[Formula: see text]+[Formula: see text]1)-dimensional Korteweg–de Vries (KdV) equation are obtained. The interaction between a lump-type soliton and a stripe soliton including two phenomena: fission and fusion, are illustrated. The dynamical behaviors are shown more intuitively by graphics.

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.

Non-traveling lump solutions and mixed lump–kink solutions to (2+1)-dimensional variable-coefficient Caudrey–Dodd–Gibbon–Kotera–Sawada equation

2019 ◽  
Vol 33 (22) ◽  
pp. 1950262 ◽  
Author(s):  
Jing Wang ◽  
Hong-Li An ◽  
Biao Li
Keyword(s):  
Variable Coefficient ◽  
Quadratic Function ◽  
Lump Solution ◽  
Lump Solutions ◽  
Interaction Solutions ◽  
Hyperbolic Cosine ◽  
Hirota Bilinear Form ◽  
Dimensional Variable ◽  
Hyperbolic Cosine Function ◽  
Hirota Bilinear

Through Hirota bilinear form and symbolic computation with Maple, we investigate some non-traveling lump and mixed lump–kink solutions of the (2[Formula: see text]+[Formula: see text]1)-dimensional variable-coefficient Caudrey–Doddy–Gibbon–Kotera–Sawada equation by an extended method. Firstly, the non-traveling lump solutions are directly obtained by taking the function [Formula: see text] as a quadratic function. Secondly, we can get the interaction solutions for a lump solution and one kink solution by taking [Formula: see text] as a combination of quadratic function and exponential function. Finally, the interaction solutions between a lump solution and a pair of kinks solution can be derived by taking [Formula: see text] as a combination of quadratic function and hyperbolic cosine function. The dynamic phenomena of the above three types of exact solutions are demonstrated by some figures.

scholarly journals Exact Solutions to a Generalized Bogoyavlensky-Konopelchenko Equation via Maple Symbolic Computations

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-6 ◽  
Author(s):  
Shou-Ting Chen ◽  
Wen-Xiu Ma
Keyword(s):  
Nonlinear Equation ◽  
Traveling Wave ◽  
Computer Algebra System ◽  
Traveling Wave Solutions ◽  
Explicit Solutions ◽  
Symbolic Computations ◽  
Wave Solutions ◽  
Hirota Bilinear Form ◽  
Hirota Bilinear ◽  
Bilinear Equation

We aim to construct exact and explicit solutions to a generalized Bogoyavlensky-Konopelchenko equation through the Maple computer algebra system. The considered nonlinear equation is transformed into a Hirota bilinear form, and symbolic computations are made for solving both the nonlinear equation and the corresponding bilinear equation. A few classes of exact and explicit solutions are generated from different ansätze on solution forms, including traveling wave solutions, two-wave solutions, and polynomial solutions.

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