Bounded traveling waves of the Burgers–Huxley equation

Zhou, Yuqian; Liu, Qian; Zhang, Weinian

doi:10.1016/j.na.2010.09.012

Cited by 11 publications

(7 citation statements)

References 18 publications

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“…This is similar to a Huxley nonlinearity, although not for the typical range of the Huxley parameters. Such equations reflect the complex interplay between the nonlinearity, convection, and diffusive transport for waves propagating in biological and chemical systems [21,22]. The solutions are obtained from…”

Section: Burgers-huxley Type Equationmentioning

confidence: 99%

Integrable dissipative nonlinear second order differential equations via factorizations and Abel equations

Mancas

Rosu

2013

Physics Letters A

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We emphasize two connections, one well known and another less known, between the dissipative nonlinear second order differential equations and the Abel equations which in its first kind form have only cubic and quadratic terms. Then, employing an old integrability criterion due to Chiellini, we introduce the corresponding integrable dissipative equations. For illustration, we present the cases of some integrable dissipative Fisher, nonlinear pendulum, and Burgers-Huxley type equations which are obtained in this way and can be of interest in applications. We also show how to obtain Abel solutions directly from the factorization of second-order nonlinear equations.

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Section: Burgers-huxley Type Equationmentioning

confidence: 99%

Integrable dissipative nonlinear second order differential equations via factorizations and Abel equations

Mancas

Rosu

2013

Physics Letters A

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“…This phenomenon was considered in [27]. The first-order Melnikov function was used to find the isolated zeros of the Melnikov function.…”

Section: Resultsmentioning

confidence: 99%

Single peak solitary wave and compacton solutions of the generalized two-component Hunter–Saxton system

Wen

Chen

2014

Nonlinear Dyn

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Dynamical system theory is applied to the generalized two-component Hunter-Saxton system. Two singular straight lines are found in the associated topological vector field. The influence of parameters as well as the singular lines on the smoothness property of the traveling wave solutions is explored in detail. We obtain the single peak solitary wave and compacton solutions for the generalized twocomponent Hunter-Saxton system. Asymptotic analysis and numerical simulations are provided for smooth solitary wave, peakon, cuspon and compacton solutions of the generalized two-component Hunter-Saxton system.

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“…Next, we consider the bounded orbit of system (6). By investigating the first integral, we see from the equilibrium points of this system that the following conclusions hold.…”

Section: Proofmentioning

confidence: 94%

On the new solutions of the generalized Burgers–Huxley equation

Wang

Guo

Lü

2016

Math Methods in App Sciences

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In this paper, we investigate a class of generalized Burgers–Huxley equation by employing the bifurcation method of planar dynamical systems. Firstly, we reduce the equation to a planar system via the traveling wave solution ansatz; then by computing the singular point quantities, we obtain the conditions of integrability and determine the existence of one stable limit cycle from Hopf bifurcation in the corresponding planar system. From this, some new exact solutions and a special periodic traveling wave solution, which is isolated as a limit, are obtained. Copyright © 2016 John Wiley & Sons, Ltd.

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Bounded traveling waves of the Burgers–Huxley equation

Cited by 11 publications

References 18 publications

Integrable dissipative nonlinear second order differential equations via factorizations and Abel equations

Integrable dissipative nonlinear second order differential equations via factorizations and Abel equations

Single peak solitary wave and compacton solutions of the generalized two-component Hunter–Saxton system

On the new solutions of the generalized Burgers–Huxley equation

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