scholarly journals LS method and qualitative analysis of traveling wave solutions of Fisher equation

2010 ◽  
Vol 59 (2) ◽  
pp. 744
Author(s):  
Li Xiang-Zheng ◽  
Zhang Wei-Guo ◽  
Yuan San-Ling
Keyword(s):  
Qualitative Analysis ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Fisher Equation ◽  
Wave Solutions

Exact Cuspon and Compactons of the Novikov Equation

2014 ◽  
Vol 24 (03) ◽  
pp. 1450037 ◽  
Author(s):  
Jibin Li
Keyword(s):  
Dynamical Systems ◽  
Qualitative Analysis ◽  
Traveling Wave ◽  
Wave Solution ◽  
Traveling Wave Solutions ◽  
Phase Portraits ◽  
Breaking Wave ◽  
Wave Solutions ◽  
Novikov Equation

In this paper, we apply the method of dynamical systems to the traveling wave solutions of the Novikov equation. Through qualitative analysis, we obtain bifurcations of phase portraits of the traveling system and exact cuspon wave solution, as well as a family of breaking wave solutions (compactons). We find that the corresponding traveling system of Novikov equation has no one-peakon solution.

A bounded and monotone finite-difference solution of a hyperbolic Burgers–Fisher equation

2018 ◽  
Vol 29 (12) ◽  
pp. 1850122
Author(s):  
L. A. Flores-Oropeza ◽  
A. Román-Loera ◽  
Ahmed S. Hendy
Keyword(s):  
Differential Equation ◽  
Finite Difference ◽  
Traveling Wave ◽  
Boundary Data ◽  
Traveling Wave Solutions ◽  
Initial Boundary ◽  
Fisher Equation ◽  
Wave Solutions ◽  
Nonlinear Advection ◽  
Finite Difference Solution

In this work, a nonlinear finite-difference scheme is provided to approximate the solutions of a hyperbolic generalization of the Burgers–Fisher equation from population dynamics. The model under study is a partial differential equation with nonlinear advection, reaction and damping terms. The existence of some traveling-wave solutions for this model has been established in the literature. In the present manuscript, we investigate the capability of our technique to preserve some of the most important features of those solutions, namely, the positivity, the boundedness and the monotonicity. The finite-difference approach followed in this work employs the exact solutions to prescribe the initial-boundary data. In addition to providing good approximations to the analytical solutions, our simulations suggest that the method is also capable of preserving the mathematical features of interest.

TRAVELING WAVE SOLUTIONS OF THE GREEN–NAGHDI SYSTEM

2013 ◽  
Vol 23 (05) ◽  
pp. 1350087 ◽  
Author(s):  
SHENGFU DENG ◽  
BOLING GUO ◽  
TINGCHUN WANG
Keyword(s):  
Qualitative Analysis ◽  
Traveling Wave ◽  
Autonomous Systems ◽  
Traveling Wave Solutions ◽  
Phase Portraits ◽  
Equivalent System ◽  
Wave Solutions ◽  
Analysis Methods

We investigate the traveling wave solutions of the Green–Naghdi system. Using the qualitative analysis methods of planar autonomous systems, we show not only its phase portraits but also the exact expressions of some bounded wave solutions. These results are a complement of the work by Deng et al. [2011], which studied the traveling wave solutions of its equivalent system under some conditions.

SOME TRAVELING WAVE SOLITONS OF THE GREEN–NAGHDI SYSTEM

2011 ◽  
Vol 21 (02) ◽  
pp. 575-585 ◽  
Author(s):  
SHENGFU DENG ◽  
BOLING GUO ◽  
TINGCHUN WANG
Keyword(s):  
Qualitative Analysis ◽  
Traveling Wave ◽  
Autonomous Systems ◽  
Traveling Wave Solutions ◽  
Periodic Wave ◽  
Phase Portraits ◽  
Equivalent System ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Soliton Wave Solutions

The traveling wave solutions for an equivalent system of the Green–Naghdi system are considered. The qualitative analysis methods of planar autonomous systems yield their phase portraits. The exact expressions of smooth soliton wave solutions, cusp soliton wave solutions, smooth periodic wave solutions and periodic cusp wave solutions are obtained. Some numerical simulations of these solutions are also given. These reveal some new properties of the Green–Naghdi system.

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