scholarly journals Exact Traveling Wave Solutions of Nonlinear Evolution Equations: Indeterminant Homogeneous Balance and Linearizability

2019 ◽  
Vol 7 (1) ◽  
pp. 10-13 ◽  
Author(s):  
Barbara Abraham-Shrauner
Keyword(s):  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Nonlinear Evolution Equations ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Homogeneous Balance

scholarly journals The Generalized Projective Riccati Equations Method for Solving Nonlinear Evolution Equations in Mathematical Physics

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
E. M. E. Zayed ◽  
K. A. E. Alurrfi
Keyword(s):  
Traveling Wave ◽  
Evolution Equations ◽  
Burgers Equation ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Riccati Equations ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions

We apply the generalized projective Riccati equations method to find the exact traveling wave solutions of some nonlinear evolution equations with any-order nonlinear terms, namely, the nonlinear Pochhammer-Chree equation, the nonlinear Burgers equation and the generalized, nonlinear Zakharov-Kuznetsov equation. This method presents wider applicability for handling many other nonlinear evolution equations in mathematical physics.

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.

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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