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 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.

scholarly journals New Exact Solutions for New Model Nonlinear Partial Differential Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-16
Author(s):  
A. Maher ◽  
H. M. El-Hawary ◽  
M. S. Al-Amry
Keyword(s):  
Nonlinear Partial Differential Equation ◽  
Elliptic Functions ◽  
Rational Functions ◽  
Travelling Wave ◽  
Mapping Method ◽  
Travelling Wave Solutions ◽  
Trigonometric Functions ◽  
Hyperbolic Functions ◽  
New Exact Solutions ◽  
New Form

In this paper we propose a new form of Padé-II equation, namely, a combined Padé-II and modified Padé-II equation. The mapping method is a promising method to solve nonlinear evaluation equations. Therefore, we apply it, to solve the combined Padé-II and modified Padé-II equation. Exact travelling wave solutions are obtained and expressed in terms of hyperbolic functions, trigonometric functions, rational functions, and elliptic functions.

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 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.

On the Exact Soliton Solutions of Some Nonlinear PDE by Tan-Cot Method

2018 ◽  
Vol 5 (1) ◽  
pp. 31-36
Author(s):  
Md Monirul Islam ◽  
Muztuba Ahbab ◽  
Md Robiul Islam ◽  
Md Humayun Kabir
Keyword(s):  
Solitary Wave ◽  
Acoustic Waves ◽  
Water Waves ◽  
Wave Equations ◽  
Rectangular Channel ◽  
Soliton Solutions ◽  
Boussinesq Equations ◽  
Travelling Wave ◽  
Ion Acoustic Waves ◽  
Analytical System

For many solitary wave applications, various approximate models have been proposed. Certainly, the most famous solitary wave equations are the K-dV, BBM and Boussinesq equations. The K-dV equation was originally derived to describe shallow water waves in a rectangular channel. Surprisingly, the equation also models ion-acoustic waves and magneto-hydrodynamic waves in plasmas, waves in elastic rods, equatorial planetary waves, acoustic waves on a crystal lattice, and more. If we describe all of the above situation, we must be needed a solution function of their governing equations. The Tan-cot method is applied to obtain exact travelling wave solutions to the generalized Korteweg-de Vries (gK-dV) equation and generalized Benjamin-Bona- Mahony (BBM) equation which are important equations to evaluate wide variety of physical applications. In this paper we described the soliton behavior of gK-dV and BBM equations by analytical system especially using Tan-cot method and shown in graphically. GUB JOURNAL OF SCIENCE AND ENGINEERING, Vol 5(1), Dec 2018 P 31-36

scholarly journals N-soliton solutions and the Hirota conditions in (1 + 1)-dimensions

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Wen-Xiu Ma
Keyword(s):  
Common Factors ◽  
Soliton Solutions ◽  
Higher Order ◽  
Kdv Equations ◽  
The Common ◽  
Bilinear Formulation ◽  
Generalized Kdv Equations ◽  
Hirota Bilinear

Abstract We analyze N-soliton solutions and explore the Hirota N-soliton conditions for scalar (1 + 1)-dimensional equations, within the Hirota bilinear formulation. An algorithm to verify the Hirota conditions is proposed by factoring out common factors out of the Hirota function in N wave vectors and comparing degrees of the involved polynomials containing the common factors. Applications to a class of generalized KdV equations and a class of generalized higher-order KdV equations are made, together with all proofs of the existence of N-soliton solutions to all equations in two classes.

Tunnelling Effects of Solitons in Optical Fibers with Higher-Order Effects

2012 ◽  
Vol 67 (6-7) ◽  
pp. 338-346
Author(s):  
Chao-Qing Dai ◽  
Hai-Ping Zhu ◽  
Chun-Long Zheng
Keyword(s):  
Optical Fibers ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Higher Order ◽  
Order Effects ◽  
Bright Solitons ◽  
Dark Solitons ◽  
Tunnelling Effect ◽  
Tunnelling Effects ◽  
Higher Order Effects

We construct four types of analytical soliton solutions for the higher-order nonlinear Schrödinger equation with distributed coefficients. These solutions include bright solitons, dark solitons, combined solitons, and M-shaped solitons. Moreover, the explicit functions which describe the evolution of the width, peak, and phase are discussed exactly.We finally discuss the nonlinear soliton tunnelling effect for four types of femtosecond solitons

New Exact Solutions for Two Nonlinear Equations

2006 ◽  
Vol 61 (1-2) ◽  
pp. 1-6 ◽  
Author(s):  
Zonghang Yang
Keyword(s):  
Wave Equation ◽  
Partial Differential Equations ◽  
Exact Solutions ◽  
Water Wave ◽  
Function Method ◽  
Nonlinear Partial Differential Equations ◽  
Soliton Solutions ◽  
New Exact Solutions ◽  
Complex Phenomena ◽  
Sivashinsky Equation

Nonlinear partial differential equations are widely used to describe complex phenomena in various fields of science, for example the Korteweg-de Vries-Kuramoto-Sivashinsky equation (KdV-KS equation) and the Ablowitz-Kaup-Newell-Segur shallow water wave equation (AKNS-SWW equation). To our knowledge the exact solutions for the first equation were still not obtained and the obtained exact solutions for the second were just N-soliton solutions. In this paper we present kinds of new exact solutions by using the extended tanh-function method.

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