Solitary wave solutions along with Painleve analysis for the Ablowitz–Kaup–Newell–Segur water waves equation

2021 ◽  
Author(s):  
Syed T. R. Rizvi ◽  
Aly R. Seadawy ◽  
U. Akram ◽  
M. Younis ◽  
Ali Althobaiti
Keyword(s):  
Water Waves ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Nonlinear Evolution Equations ◽  
Auxiliary Equation ◽  
Solitary Wave Solutions ◽  
Painlevé Test ◽  
Wave Solutions ◽  
Akns Equation

This study focuses on the Ablowitz–Kaup–Newell–Segur (AKNS) water waves equation. Painleve test (P-test) will be implemented to check the integrability of AKNS equation and an extended modified auxiliary equation mapping (EMAEM) architectonic is implemented to get a new set of traveling wave solutions like periodic and doubly periodic, bell type, kink, singular kink, anti-kink, trigonometric, singular, rational, combined soliton like solutions and hyperbolic solutions. Furthermore, it is analyzed that the implemented algorithm is efficient and accurate for solving nonlinear evolution equations (NLEEs). Finally, graphical simulations (2D, 3D and contours) are also provided to illustrate the detailed behavior of the solution and effectiveness of the proposed method.

scholarly journals Solitary Wave Solutions of Some Coupled Nonlinear Evolution Equations

2014 ◽  
Vol 6 (2) ◽  
pp. 273-284 ◽  
Author(s):  
K. Khan ◽  
M. A. Akbar
Keyword(s):  
Solitary Wave ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Long Wave

In this article, the modified simple equation (MSE) method has been executed to find the traveling wave solutions of the coupled (1+1)-dimensional Broer-Kaup (BK) equations and the dispersive long wave (DLW) equations. The efficiency of the method for finding exact solutions has been demonstrated. It has been shown that the method is direct, effective and can be used for many other nonlinear evolution equations (NLEEs) in mathematical physics. Moreover, this procedure reduces the large volume of calculations.  Keywords: MSE method; NLEE; BK equations; DLW equations; Solitary wave solutions. © 2014 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. doi: http://dx.doi.org/10.3329/jsr.v6i2.16671 J. Sci. Res. 6 (2), 273-284 (2014)  

GENERALIZED EXTENDED TANH-FUNCTION METHOD TO CONSTRUCT NEW EXPLICIT EXACT SOLUTIONS FOR THE APPROXIMATE EQUATIONS FOR LONG WATER WAVES

2003 ◽  
Vol 14 (05) ◽  
pp. 601-611 ◽  
Author(s):  
YONG CHEN ◽  
ZHENG YU
Keyword(s):  
Exact Solutions ◽  
Water Waves ◽  
Algebraic System ◽  
Function Method ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Approximate Equations

In this paper, a generalized extended tanh-function method for constructing exact solutions of nonlinear evolution equations (NEEs) is presented and implemented in a computer algebraic system. Applying the generalized method, with the aid of Maple, we consider the system of the approximate equations for long water waves and find the new more general explicit exact solutions. The properties of the new solitary wave solutions are shown by some figures.

EXACT TRAVELING WAVE SOLUTIONS FOR SOME NONLINEAR EVOLUTION EQUATIONS WITH NONLINEAR TERMS OF ANY ORDER

2003 ◽  
Vol 14 (01) ◽  
pp. 99-112 ◽  
Author(s):  
YONG CHEN ◽  
BIAO LI ◽  
HONG-QING ZHANG
Keyword(s):  
Solitary Wave ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Nonlinear Evolution Equations ◽  
Solitary Wave Solutions ◽  
Rational Solutions ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions

In this paper, we improved the tanh method by means of a proper transformation and general ansätz. Using the improved method, with the aid of Mathematica™, we consider some nonlinear evolution equations with nonlinear terms of any order. As a result, rich explicit exact traveling wave solutions for these equations, which contain kink profile solitary wave solutions, bell profile solitary wave solutions, rational solutions, periodic solutions, and combined formal solutions, are obtained.

scholarly journals Mathematical modeling of DNA vibrational dynamics and its solitary wave solutions

2018 ◽  
Vol 64 (6) ◽  
pp. 590 ◽  
Author(s):  
Reza Abazari ◽  
Shabnam Jamshidzadeh ◽  
Gangwei Wang
Keyword(s):  
Mathematical Modeling ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Nonlinear Evolution Equations ◽  
Solitary Wave Solutions ◽  
Vibrational Dynamics ◽  
Wave Solutions ◽  
Vibration Dynamics

In this work, the traveling wave solutions of a mathematical modeling of DNA vibration dynamics proposed by Peyrard-Bishop, that takes into consideration the inclusion of nonlinear interaction between adjacent displacements along the Hydrogen bonds, is investigated by both $(G'/G)$-expansion and $F$-expansion methods. Using these methods, some new explicit forms of traveling wave solutions of present nonlinear equation are given. The methods come in to be easier and faster by means of a symbolic computation and yield powerful mathematical tools for solving nonlinear evolution equations in many branches of sciences, especially physics, biology and etc.

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.

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