scholarly journals Unified method applied to the new Hamiltonian amplitude equation: Wave solutions and stability analysis

2021 ◽  
Author(s):  
Islam S M Rayhanul
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Wave Train ◽  
Three Dimensional ◽  
Nonlinear Evolution Equations ◽  
Main Task ◽  
Propagation Characteristics ◽  
Wave Solutions ◽  
Trigonometric Function Solutions ◽  
Unified Method

Abstract The new Hamiltonian amplitude (nHA) equation deals with some of the disabilities of the modulation wave-train. The main task of this paper is to extract the analytical wave solutions of the nHA equation. Based on the unified scheme, analytical wave solutions are attained in terms of hyperbolic and trigonometric function solutions. In order to prompt the underlying wave propagation characteristics, three-dimensional (3D), two-dimensional (2D) are illustrated from the solutions obtained with the help of computational packages Mathematica and also made comparisons between wave profiles for various values. The proposed method can also be used for many other nonlinear evolution equations.

NEW TRAVELING WAVE SOLUTIONS FOR A CLASS OF NONLINEAR EVOLUTION EQUATIONS

2011 ◽  
Vol 25 (02) ◽  
pp. 319-327 ◽  
Author(s):  
CHENG-JIE BAI ◽  
HONG ZHAO ◽  
HENG-YING XU ◽  
XIA ZHANG
Keyword(s):  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Mapping Method ◽  
Nonlinear Evolution Equations ◽  
Wave Solutions ◽  
Trigonometric Function Solutions ◽  
Klein Gordon ◽  
Transformation Relation

The deformation mapping method is extended to solve a class of nonlinear evolution equations (NLEEs). Many types of explicit and exact traveling wave solutions, which contain solitary wave solutions, trigonometric function solutions, and Jacobian elliptic function solutions, are obtained by a simple algebraic transformation relation between the solutions of the NLEEs and those of the cubic nonlinear Klein–Gordon (NKG) equation.

Construction of the numerical and analytical wave solutions of the Joseph–Egri dynamical equation for the long waves in nonlinear dispersive systems

2020 ◽  
Vol 34 (30) ◽  
pp. 2050289
Author(s):  
Abdulghani R. Alharbi ◽  
M. B. Almatrafi ◽  
Aly R. Seadawy
Keyword(s):  
Solitary Wave ◽  
Numerical Solution ◽  
Evolution Equations ◽  
Dynamical Equation ◽  
Nonlinear Evolution ◽  
Three Dimensional ◽  
Nonlinear Evolution Equations ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
The Stability

The Kudryashov technique is employed to extract several classes of solitary wave solutions for the Joseph–Egri equation. The stability of the achieved solutions is tested. The numerical solution of this equation is also investigated. We also present the accuracy and the stability of the numerical schemes. Some two- and three-dimensional figures are shown to present the solutions on some specific domains. The used methods are found useful to be applied on other nonlinear evolution equations.

scholarly journals The unified method for abundant soliton solutions of local time fractional nonlinear evolution equations

2021 ◽  
Vol 22 ◽  
pp. 103979
Author(s):  
Nauman Raza ◽  
Muhammad Hamza Rafiq ◽  
Melike Kaplan ◽  
Sunil Kumar ◽  
Yu-Ming Chu
Keyword(s):  
Local Time ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Nonlinear Evolution Equations ◽  
The Unified Method ◽  
Unified Method

Explicit, periodic and dispersive soliton solutions to the conformable time-fractional Wu–Zhang system

2021 ◽  
pp. 2150417
Author(s):  
Kalim U. Tariq ◽  
Mostafa M. A. Khater ◽  
Muhammad Younis
Keyword(s):  
Fractional Derivative ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Nonlinear Evolution Equations ◽  
Conformable Fractional Derivative ◽  
Physical Behavior ◽  
Wave Solutions

In this paper, some new traveling wave solutions to the conformable time-fractional Wu–Zhang system are constructed with the help of the extended Fan sub-equation method. The conformable fractional derivative is employed to transform the fractional form of the system into ordinary differential system with an integer order. Some distinct types of figures are sketched to illustrate the physical behavior of the obtained solutions. The power and effective of the used method is shown and its ability for applying different forms of nonlinear evolution equations is also verified.

W-shape bright and several other solutions to the (3+1)-dimensional nonlinear evolution equations

2021 ◽  
pp. 2150468
Author(s):  
Youssoufa Saliou ◽  
Souleymanou Abbagari ◽  
Alphonse Houwe ◽  
M. S. Osman ◽  
Doka Serge Yamigno ◽  
...  
Keyword(s):  
Acoustic Waves ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Singular Function ◽  
Ion Acoustic Waves ◽  
Weakly Nonlinear ◽  
Quantum Electron ◽  
Ion Acoustic ◽  
Trigonometric Function Solutions

By employing the Modified Sardar Sub-Equation Method (MSEM), several solitons such as W-shape bright, dark solitons, trigonometric function solutions and singular function solutions have been obtained in two famous nonlinear evolution equations which are used to describe waves in quantum electron–positron–ion magnetoplasmas and weakly nonlinear ion-acoustic waves in a plasma. These models are the (3+1)-dimensional nonlinear extended quantum Zakharov–Kuznetsov (NLEQZK) equation and the (3+1)-dimensional nonlinear modified Zakharov–Kuznetsov (NLmZK) equation, respectively. Comparing the obtained results with Refs. 32–34 and Refs. 43–46, additional soliton-like solutions have been retrieved and will be useful in future to explain the interaction between lower nonlinear ion-acoustic waves and the parameters of the MSEM and the obtained figures will have more physical explanation.

Sign in / Sign up

Export Citation Format

Share Document