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Explicit travelling-wave solutions

2004
A number of explicit nontrivial monotonic travelling-wave solutions of the nonlinear reaction-convection-diffusion equation (1.1) have been discovered by various authors. It is not the intention here to provide a survey of all these. However, a few remarks on the possibilities offered by the now apparent correspondence between travelling-wave solutions
Brian H. Gilding, Robert Kersner
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Traveling wave solutions for reaction–diffusion systems

Nonlinear Analysis: Theory, Methods & Applications, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lin, Zhigui   +2 more
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The Smooth and Nonsmooth Travelling Wave Solutions in a Nonlinear Wave Equation

Applied Mathematics and Mechanics, 2001
This paper is devoted to the travelling wave solutions (TWS) for a class of PDE. Travelling wave for this PDE is a planar cubic polynomial system in three--parameter space. Using the theory of planar dynamical systems, the author obtains all topological classifications of the cubic polynomial system.
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Travelling Wave Solutions for sine-Gordon Prototypes

International Journal of Nonlinear Sciences and Numerical Simulation, 2001
Summary: By using finite difference discretization for the sine-Gordon equation, we obtain the sine-Gordon prototypes. For these prototypes, the existence of discrete periodic travelling wave solutions and discrete solitons are proved by the anti-integrable limit method.
Zheng, Yongai   +2 more
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Traveling Wave Solution for a Hyperbolic Differential Equation

Lobachevskii Journal of Mathematics
The existence of weak and strong detonation waves for a version of the Majda's model is proved. In fact, the existence of traveling wave solutions for an exothermic combustion involving more than one reaction is studied.
Razani, Abdolrahman   +1 more
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Traveling-wave solutions to thin-film equations

Physical Review E, 1993
Thin films can be effectively described by the lubrication approximation, in which the equation of motion is ${\mathit{h}}_{\mathit{t}}$+(${\mathit{h}}^{\mathit{n}}$${\mathit{h}}_{\mathit{x}\mathit{x}\mathit{x}}$${)}_{\mathit{x}}$=0. Here h is a necessarily positive quantity which represents the height or thickness of the film.
, Boatto, , Kadanoff, , Olla
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Travelling wave solutions to the Kuramoto–Sivashinsky equation

Chaos, Solitons & Fractals, 2007
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Travelling-wave solution in the Rapoport–Leas model

Analysis and Mathematical Physics, 2017
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A travelling wave solution to the kolmogorov equation with noise

Stochastics and Stochastic Reports, 1996
Preprint: Weierstraß-Institut für Angewandte Analysis und Stochastik, vol ...
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On Solutions of the Travelling Wave Type in a Transportation Model

Automation and Remote Control, 2003
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