Lump-periodic, some interaction phenomena and breather wave solutions to the (2+1)-rth dispersionless Dym equation

2021 ◽  
Author(s):  
Muhammad Bilal ◽  
Shafqat Ur-Rehman ◽  
Jamshad Ahmad
Keyword(s):  
Water Waves ◽  
Three Dimensional ◽  
Hirota’S Bilinear Method ◽  
Bilinear Method ◽  
Test Function ◽  
Wave Solutions ◽  
Higher Dimensional ◽  
Engineering Sciences ◽  
Dym Equation ◽  
Nonlinear Fluid

In this study, we successfully apply Hirota’s bilinear method (HBM) to retrieve the different wave structures of the general [Formula: see text]th dispersionless Dym equation by considering the test function approaches. The studied model is used to describe the dynamics of deep water waves. We formally retrieve some novel lump periodic, some other new interaction, and breather wave solutions. Moreover, the physical behavior of the reported results is sketched through several three-dimensional, two-dimensional and contour profiles with the assistance of suitable parameters. The acquired results are valuable in grasping the elementary scenarios of nonlinear fluid dynamics as well as the dynamics of engineering sciences in the related nonlinear higher-dimensional wave fields. The gained results are checked and found correct by putting them into the governing equation with the aid of Mathematica. Thus, our strategies through the fortress of representative calculations give a functioning and intense mathematical execution for tackling complicated nonlinear wave issues.

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.

Multiple rogue and soliton wave solutions to the generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt equation arising in fluid mechanics and plasma physics

2021 ◽  
pp. 2150383
Author(s):  
Onur Alp Ilhan ◽  
Sadiq Taha Abdulazeez ◽  
Jalil Manafian ◽  
Hooshmand Azizi ◽  
Subhiya M. Zeynalli
Keyword(s):  
Rogue Wave ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
The Novel ◽  
Algebraic Equations ◽  
Bilinear Method ◽  
Dynamical Characteristics ◽  
Wave Solutions ◽  
Multiple Soliton Solutions ◽  
Soliton Wave Solutions

Under investigation in this paper is the generalized Konopelchenko–Dubrovsky–Kaup-Kupershmidt equation. Based on bilinear method, the multiple rogue wave (RW) solutions and the novel multiple soliton solutions are constructed by giving some specific activation functions for the considered model. By means of symbolic computation, these analytical solutions and corresponding rogue wave solutions are obtained via Maple 18 software. The exact lump and RW solutions, by solving the under-determined nonlinear system of algebraic equations for the specified parameters, will be constructed. Via various three-dimensional plots and density plots, dynamical characteristics of these waves are exhibited.

Three-Dimensional Weakly Nonlinear Shallow Water Waves Regime and its Traveling Wave Solutions

2018 ◽  
Vol 15 (03) ◽  
pp. 1850017 ◽  
Author(s):  
Aly R. Seadawy
Keyword(s):  
Free Surface ◽  
Solitary Wave ◽  
Shallow Water ◽  
Traveling Wave ◽  
Water Waves ◽  
Three Dimensional ◽  
Traveling Wave Solutions ◽  
Shallow Water Waves ◽  
Weakly Nonlinear ◽  
Wave Solutions

The problem formulations of models for three-dimensional weakly nonlinear shallow water waves regime in a stratified shear flow with a free surface are studied. Traveling wave solutions are generated by deriving the nonlinear higher order of nonlinear evaluation equations for the free surface displacement. We obtain the velocity potential and pressure fluid in the form of traveling wave solutions of the obtained nonlinear evaluation equation. The obtained solutions and the movement role of the waves of the exact solutions are new travelling wave solutions in different and explicit form such as solutions (bright and dark), solitary wave, periodic solitary wave elliptic function solutions of higher-order nonlinear evaluation equation.

Multi and breather wave soliton solutions and the linear superposition principle for generalized Hietarinta equation

2022 ◽  
Author(s):  
S. Şule Şener Kiliç
Keyword(s):  
Asymptotic Behavior ◽  
Superposition Principle ◽  
Soliton Solutions ◽  
Asymptotic Behavior Of Solutions ◽  
Hirota’S Bilinear Method ◽  
Bilinear Method ◽  
Linear Superposition ◽  
Wave Solutions ◽  
Linear Superposition Principle ◽  
Soliton Wave Solutions

In this paper, we study the generalized ([Formula: see text])-dimensional Hietarinta equation which is investigated by utilizing Hirota’s bilinear method. Also, the bilinear form is obtained, and the N-soliton solutions are constructed. In addition, multi-wave and breather wave solutions of the addressed equation with specific coefficients are presented. Finally, under certain conditions, the asymptotic behavior of solutions is analyzed in both methods. Moreover, we employ the linear superposition principle to determine [Formula: see text]-soliton wave solutions for the generalized ([Formula: see text])-dimensional Hietarinta equation.

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.

Modulational instability and multiple rogue wave solutions for the generalized CBS-BK equation

2021 ◽  
pp. 2150408
Author(s):  
Wang Gang ◽  
Jalil Manafian ◽  
Fatma Berna Benli ◽  
Onur Alp İlhan ◽  
Reza Goldaran
Keyword(s):  
Asymptotic Behavior ◽  
Multiple Solutions ◽  
Modulation Instability ◽  
Rogue Wave ◽  
Modulational Instability ◽  
Soliton Solutions ◽  
Hirota’S Bilinear Method ◽  
Bilinear Method ◽  
Wave Solutions ◽  
Multiple Soliton Solutions

An integrable of the generalized Calogero-Bogoyavlenskii-Schiff-Bogoyavlensky-Konopelchenko (CBS-BK) equation is studied, by employing Hirota’s bilinear method the bilinear form is obtained, and the multiple-soliton solutions are constructed. The modified of improved bilinear method has been utilized to investigate multiple solutions. In addition, some graphs including 3D, contour, density, and [Formula: see text]-curves plots of the addressed equation with specific coefficients are shown. Finally, under certain conditions, the asymptotic behavior of the linearization solution is analyzed to prove that the modulation instability is stable for some points.

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.

scholarly journals Rational Wave Solutions and Dynamics Properties of the Generalized ( 2 + 1 )-Dimensional Calogero-Bogoyavlenskii-Schiff Equation by Using Bilinear Method

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Lihui Han ◽  
Sudao Bilige Bilige ◽  
Xiaomin Wang ◽  
Meiyu Li ◽  
Runfa Zhang
Keyword(s):  
Exact Solutions ◽  
Symbolic Computation ◽  
Three Dimensional ◽  
Bilinear Operator ◽  
Bilinear Method ◽  
Wave Solutions ◽  
Contour Plots ◽  
Scientific Phenomena

Through symbolic computation with Maple, fifty-seven sets of rational wave solutions to the generalized Calogero-Bogoyavlenskii-Schiff equation are presented by employing the generalized bilinear operator when the parameter p = 2 . Via the three-dimensional plots and contour plots with the help of Maple, the dynamics of these solutions are described very well. These solutions have greatly enriched the exact solutions of the generalized Calogero-Bogoyavlenskii-Schiff equation on the existing literature. The result will be widely used to describe many nonlinear scientific phenomena.

Emergence and Interaction of the Lump-Type Solution with the (3+1)-D Jimbo-Miwa Equation

2017 ◽  
Vol 73 (1) ◽  
pp. 43-49 ◽  
Author(s):  
Wei Tan ◽  
Zheng-de Dai ◽  
Jing-li Xie ◽  
Ling-li Hu
Keyword(s):  
Exact Solutions ◽  
Soliton Solution ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
Hirota’S Bilinear Method ◽  
Type Solution ◽  
Bilinear Method ◽  
Limit Behaviour

AbstractA kinky breather-soliton solution and kinky periodic-soliton solution are obtained using Hirota’s bilinear method and homoclinic test approach for the (3+1)-dimensional Jimbo-Miwa equation. Based on these two exact solutions, some lump-type solutions are emerged by limit behaviour. Meanwhile, two kinds of new dynamical phenomena, kinky breather degeneracy and kinky periodic degeneracy, are discussed and presented. Finally, the interaction between a stripe soliton and a lump-type soliton is discussed by the standardisation of the lump-type solution; the fusion and fission phenomena of soliton solutions are investigated and simulated by three-dimensional plots.

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