scholarly journals Some new soliton solutions of time fractional resonant Davey-Stewartson equations

2021 ◽  
Author(s):  
Esin Ilhan
Keyword(s):  
Traveling Wave ◽  
Soliton Solutions ◽  
Travelling Wave ◽  
Traveling Wave Solution ◽  
New Exact Solutions ◽  
Wolfram Mathematica ◽  
Liouville Fractional Derivative ◽  
Homogeneous Balance Method ◽  
In The Beginning ◽  
Homogeneous Balance

In this study, via the Bernoulli sub-equation, the analytical traveling wave solution of the (2+1)-dimensional resonant Davey-Stewartson system is investigated. In the beginning, Based on the Riemann-Liouville fractional derivative, the time-fractional imaginary (2+1)-dimensional resonant Davey-Stewatson equation by using travelling wave is changed into a nonlinear differential system. The homogeneous balance method between the highest power terms and the highest derivative of the ordinary differential equation is authorized on the resultant outcome equation, and finally, the ordinary differential equations are solved to obtain some new exact solutions. Different cases, as well as different values of physical constants to investigate the optical soliton solutions of the resulting system, are used. The outcomes results of this study are shown in 3D dimensions graphically via Wolfram Mathematica Package.

Abundant New Multiple Soliton-like Solutions and Rational Solutions of the (2+1)-Dimensional Broer-Kaup Equation

2001 ◽  
Vol 56 (12) ◽  
pp. 816-824 ◽  
Author(s):  
Zhenya Yan
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Bäcklund Transformation ◽  
Soliton Solutions ◽  
Nonlinear Evolution Equations ◽  
Heat Equations ◽  
Backlund Transformation ◽  
Rational Solutions ◽  
Homogeneous Balance Method ◽  
Homogeneous Balance

Abstract In this paper we firstly improve the homogeneous balance method due to Wang, which was only used to obtain single soliton solutions of nonlinear evolution equations, and apply it to (2 + 1)-dimensional Broer-Kaup (BK) equations such that a Backlund transformation is found again. Considering further the obtained Backlund transformation, the relations are deduced among BK equations, well-known Burgers equations and linear heat equations. Finally, abundant multiple soliton-like solutions and infinite rational solutions are obtained from the relations.

scholarly journals New exact soliton solutions, bifurcation and multistability behaviors of traveling waves for the (3+1)-dimensional modified Zakharov-Kuznetsov equation with higher order dispersion

2021 ◽  
Author(s):  
Asit Saha ◽  
Battal Gazi Karakoç ◽  
Khalid K. Ali
Keyword(s):  
Traveling Wave ◽  
Soliton Solutions ◽  
Travelling Wave ◽  
Higher Order ◽  
Physical Parameters ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Higher Order Dispersion ◽  
Order Dispersion ◽  
Bifurcation Behavior

The goal of the present paper is to obtain and analyze new exact travelling wave solutions and bifurcation behavior of modified Zakharov-Kuznetsov (mZK) equation with higher order dispersion term. For this purpose, first and second simple methods are used to build soliton solutions of travelling wave solutions. Furthermore, bifurcation behavior of traveling waves including new type of quasiperiodic and multi-periodic traveling wave motions have been examined depending on the physical parameters. Multistability for the nonlinear mZK equation has been investigated depending on fixed values of physical parameters with various initial conditions. The suggested methods for the analytical solutions are powerful and benefical tools to obtain the exact travelling wave solutions of nonlinear evolution equations (NLEEs). Two and three-dimensional plots are also provided to illustrate the new solutions. Bifurcation and multistability behaviors of traveling wave solution of the nonlinear mZK equation with higher order dispersion will add some value in the literature of mathematical and plasma physics.

Exact Traveling Wave Solutions to a Model for Solid-Solid Phase Transitions Driven by Configurational Forces

2011 ◽  
Vol 418-420 ◽  
pp. 1694-1697 ◽  
Author(s):  
Chang Hong Guo ◽  
Xiang Dong Liu ◽  
Shao Mei Fang
Keyword(s):  
Phase Transitions ◽  
Traveling Wave ◽  
Solid Phase ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Configurational Forces ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Homogeneous Balance Method ◽  
Homogeneous Balance

This paper studies the exact traveling wave solutions to a model for solid-solid phase transitions driven by configurational forces. The model consists of the partial differential equations of linear elasticity coupled to a quasilinear nonuniformly parabolic equation of second order, which describes the diffusionless phase transitions of solid materials. By using the hyperbolic tangent function expansion method and homogeneous balance method, some exact traveling wave solutions, including solitary wave solutions are obtained for the phase transitions model in one space dimension.

scholarly journals On solitary wave solutions of a peptide group system with higher order saturable nonlinearity

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 933-938
Author(s):  
Mustafa Inc ◽  
Ahmed Elhassanein ◽  
Mohamed Aly Mohamed Abdou ◽  
Yu-Ming Chu
Keyword(s):  
Soliton Solutions ◽  
Continuous Model ◽  
Travelling Wave ◽  
Mapping Method ◽  
Higher Order ◽  
Peptide Group ◽  
Group System ◽  
Saturable Nonlinearity ◽  
Discrete Schrödinger Equation ◽  
New Exact Solutions

Abstract In this article, a new continuous model of a peptide group system with higher order saturable nonlinearity is derived. The model is constructed up on discrete Schrodinger equation with higher order saturable nonlinearity. New exact solutions of the proposed model are investigated. Via the generalized Riccati equation mapping method travelling wave and soliton solutions are derived. For certain values of parameters kink, antikink, breathers, and dark and bright solitons are presented.

scholarly journals Dark and trigonometric soliton solutions in asymmetrical Nizhnik-Novikov-Veselov equation with (2+1)-dimensional

2021 ◽  
Vol 11 (1) ◽  
pp. 92-99
Author(s):  
Haci Mehmet Baskonus
Keyword(s):  
Exponential Function ◽  
Traveling Wave ◽  
Function Method ◽  
Soliton Solutions ◽  
Trigonometric Function ◽  
Wolfram Mathematica ◽  
Waves Propagation ◽  
Exponential Function Method ◽  
2D And 3D

In this manuscript, new dark and trigonometric function traveling wave soliton solutions to the (2+1)-dimensional asymmetrical Nizhnik-Novikov-Veselov equation by using the modified exponential function method are successfully obtained. Along with novel dark structures, trigonometric solutions are also extracted. For deeper investigating of waves propagation on the surface, 2D and 3D graphs along with contour simulations via computational programs such as Wolfram Mathematica, Matlap softwares and so on are presented.

scholarly journals A general sub-equation method to the burgers-like equation

2017 ◽  
Vol 21 (4) ◽  
pp. 1681-1687 ◽  
Author(s):  
Xiao-Min Wang ◽  
Su-Dao Bilige ◽  
Yue-Xing Bai
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Equation Method ◽  
Rational Solutions ◽  
New Exact Solutions ◽  
Wave Solutions ◽  
Potential Applications

A Burgers-like equation is studied by a general sub-equation method, and some new exact solutions are obtained, which include the traveling wave solutions, non-traveling wave solutions, multi-soliton solutions, rational solutions, and other types of solutions. The obtained results are important in thermal science, and potential applications can be found.

scholarly journals SOME PROPERTIES OF FRACTIONAL BURGERS EQUATION

2002 ◽  
Vol 7 (1) ◽  
pp. 151-158 ◽  
Author(s):  
P. Miškinis
Keyword(s):  
Analytical Solution ◽  
Fractional Derivative ◽  
Conservation Laws ◽  
Traveling Wave ◽  
Wave Solution ◽  
Burgers Equation ◽  
Initial Conditions ◽  
Traveling Wave Solution ◽  
One Dimensional ◽  
Liouville Fractional Derivative

The fractional generalization of a one‐dimensional Burgers equationwith initial conditions ɸ(x, 0) = ɸ0(x); ɸt(x,0) = ψ0 (x), where ɸ = ɸ(x,t) ∈ C2(Ω): ɸt = δɸ/δt; aDx p is the Riemann‐Liouville fractional derivative of the order p; Ω = (x,t) : x ∈ E 1, t > 0; and the explicit form of a particular analytical solution are suggested. Existing of traveling wave solution and conservation laws are considered. The relation with Burgers equation of integer order and properties of fractional generalization of the Hopf‐Cole transformation are discussed.

scholarly journals On a Generalized Fifth-Order Integrable Evolution Equation and its Hierarchy

2006 ◽  
Vol 61 (1-2) ◽  
pp. 7-15
Author(s):  
Amitava Choudhuri ◽  
Benoy Talukdar ◽  
S. B. Dattab
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Hamiltonian Structures ◽  
Lagrangian Equations ◽  
Integrable Evolution Equation ◽  
Integrable Evolution ◽  
Homogeneous Balance Method ◽  
Fifth Order ◽  
Homogeneous Balance

A general form of a fifth-order nonlinear evolution equation is considered. The Helmholtz solution of the inverse variational problem is used to derive conditions under which this equation admits an analytic representation. A Lennard type recursion operator is then employed to construct a hierarchy of Lagrangian equations. It is explicitly demonstrated that the constructed system of equations has a Lax representation and two compatible Hamiltonian structures. The homogeneous balance method is used to derive analytic soliton solutions of the third- and fifth-order equations. - PACS numbers: 47.20.Ky, 42.81.Dp, 02.30.Jr

Quasi-Periodic, Periodic Waves, and Soliton Solutions for the Combined KdV-mKdV Equation

2009 ◽  
Vol 64 (9-10) ◽  
pp. 639-645 ◽  
Author(s):  
Emad A.-B. Abdel-Salam
Keyword(s):  
Elliptic Function ◽  
Function Method ◽  
Nonlinear Partial Differential Equations ◽  
Soliton Solutions ◽  
Travelling Wave ◽  
Mkdv Equation ◽  
Jacobi Elliptic Function ◽  
New Exact Solutions ◽  
De Vries ◽  
Jacobi Elliptic Function Method

By introducing the generalized Jacobi elliptic function, a new improved Jacobi elliptic function method is used to construct the exact travelling wave solutions of the nonlinear partial differential equations in a unified way. With the help of the improved Jacobi elliptic function method and symbolic computation, some new exact solutions of the combined Korteweg-de Vries-modified Korteweg-de Vries (KdV-mKdV) equation are obtained. Based on the derived solution, we investigate the evolution of doubly periodic and solitons in the background waves. Also, their structures are further discussed graphically.

scholarly journals On The Exact Solutions to Conformable Time Fractional Equations in EW Family Using Sine-Gordon Equation Approach

2017 ◽  
Author(s):  
Alper Korkmaz ◽  
Ozlem Ersoy Hepson ◽  
Kamyar Hosseini ◽  
Hadi Rezazadeh ◽  
Mostafa Eslami
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Gordon Equation ◽  
Solution Procedure ◽  
Equation Approach ◽  
Sine Gordon Equation ◽  
Hyperbolic Functions ◽  
Fractional Equations ◽  
New Exact Solutions ◽  
Homogeneous Balance

New exact solutions to conformable time fractional EW and modified EW equations are constructed by using Sine-Gordon expansion approach. The fractional traveling wave transform and homogeneous balance have significant roles in the solution procedure. The predicted solution is of the form of some finite series of multiplication of powers of cos and sin functions. The relation among trigonometric and hyperbolic functions in sense of Sine-Gordon expansion gives opportunity to construct the solutions in terms of hyperbolic functions.

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