scholarly journals Traveling wave solutions of an ordinary-parabolic system in R2 and a 2D-strip

2016 ◽  
Vol 10 (1) ◽  
pp. 208-230
Author(s):  
Yanling Tian ◽  
Chufen Wu ◽  
Zhengrong Liu
Keyword(s):  
Parabolic System ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Model System ◽  
Spreading Speeds ◽  
New Approach ◽  
Wave Speeds ◽  
Wave Solutions ◽  
Predator Model ◽  
Insight Into

We investigate a prey-predator model, which we describe by an ordinary- parabolic system. We obtain four types of wave solutions of this system, which are connecting different equilibria. To establish the existence of four types of traveling wave solutions with double wave speeds, we introduce a new approach to constructing monotonous iteration schemes. Moreover, by using spreading speeds, we establish the non-existence of traveling wave solutions. Our results provide insight into the dynamics of this model system.

scholarly journals Spreading speeds and traveling wave solutions in cooperative integral-differential systems

2015 ◽  
Vol 20 (6) ◽  
pp. 1663-1684 ◽  
Author(s):  
Changbing Hu ◽  
◽  
Yang Kuang ◽  
Bingtuan Li ◽  
Hao Liu ◽  
...  
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Spreading Speeds ◽  
Differential Systems ◽  
Wave Solutions

scholarly journals Stability of Periodic, Traveling-Wave Solutions to the Capillary Whitham Equation

Fluids ◽  
2019 ◽  
Vol 4 (1) ◽  
pp. 58 ◽  
Author(s):  
John D. Carter ◽  
Morgan Rozman
Keyword(s):  
Surface Tension ◽  
Shallow Water ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Representative Sampling ◽  
Wave Speeds ◽  
Wave Solutions ◽  
Whitham Equations ◽  
Periodic Traveling Wave ◽  
Whitham Equation

Recently, the Whitham and capillary Whitham equations were shown to accurately modelthe evolution of surface waves on shallow water. In order to gain a deeper understanding of theseequations, we compute periodic, traveling-wave solutions for both and study their stability. Wepresent plots of a representative sampling of solutions for a range of wavelengths, wave speeds, waveheights, and surface tension values. Finally, we discuss the role these parameters play in the stabilityof these solutions.

scholarly journals An application of the new function method to the Zhiber–Shabat equation

2017 ◽  
Vol 7 (3) ◽  
pp. 271-274
Author(s):  
Tolga Aktürk ◽  
Yusuf Gürefe ◽  
Yusuf Pandır
Keyword(s):  
Traveling Wave ◽  
Function Method ◽  
Elliptic Integral ◽  
Traveling Wave Solutions ◽  
Elliptic Functions ◽  
Integral Function ◽  
Jacobi Elliptic Functions ◽  
New Approach ◽  
Function Solution ◽  
Wave Solutions

This paper applies a new approach including the trial equation based on the exponential function in order to find new traveling wave solutions to Zhiber-Shabat equation. By the using of this method, we obtain a new elliptic integral function solution. Also, this solution can be converted into Jacobi elliptic functions solution by a simple transformation.

scholarly journals Traveling wave solutions in advection hyperbolic-parabolic system with nonlocal delay

2018 ◽  
Vol 23 (6) ◽  
pp. 2091-2119
Author(s):  
Kun Li ◽  
◽  
Jianhua Huang ◽  
Xiong Li ◽  
◽  
...  
Keyword(s):  
Parabolic System ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Nonlocal Delay ◽  
Wave Solutions

scholarly journals Application of the new approach of generalized (G' /G) -expansion method to find exact solutions of nonlinear PDEs in mathematical physics

BIBECHANA ◽  
2013 ◽  
Vol 10 ◽  
pp. 58-70 ◽  
Author(s):  
Md. Nur Alam ◽  
M Ali Akbar
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Nonlinear Evolution Equations ◽  
Nonlinear Pdes ◽  
Mathematical Tool ◽  
New Approach ◽  
Wave Solutions

The exact solutions of nonlinear evolution equations (NLEEs) play a crucial role to make known the internal mechanism of complex physical phenomena. In this article, we construct the traveling wave solutions of the Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZK-BBM) equation by means of the new approach of generalized (G′ /G) -expansion method. Abundant traveling wave solutions with arbitrary parameters are successfully obtained by this method and the wave solutions are expressed in terms of the hyperbolic, trigonometric, and rational functions. It is shown that the new approach of generalized (G′ /G) -expansion method is a powerful and concise mathematical tool for solving nonlinear partial differential equations. BIBECHANA 10 (2014) 58-70 DOI: http://dx.doi.org/10.3126/bibechana.v10i0.9312

scholarly journals Exact Solutions to KdV6 Equation by Using a New Approach of the Projective Riccati Equation Method

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Cesar A. Gómez S ◽  
Alvaro H. Salas ◽  
Bernardo Acevedo Frias
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Point Of View ◽  
Computational Method ◽  
New Approach ◽  
Wave Solutions ◽  
Projective Riccati Equation Method ◽  
Kdv6 Equation

We study a new integrable KdV6 equation from the point of view of its exact solutions by using an improved computational method. A new approach to the projective Riccati equations method is implemented and used to construct traveling wave solutions for a new integrable system, which is equivalent to KdV6 equation. Periodic and soliton solutions are formally derived. Finally, some conclusions are given.

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