A Fisher/KPP-type equation with density-dependent diffusion and convection: travelling-wave solutions

2005 ◽  
Vol 38 (15) ◽  
pp. 3367-3379 ◽  
Author(s):  
B H Gilding ◽  
R Kersner
Keyword(s):  
Type Equation ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Density Dependent ◽  
Wave Solutions ◽  
Diffusion And Convection

scholarly journals A study of bifurcation parameters in travelling wave solutions of a damped forced Korteweg de Vries-Kuramoto Sivashinsky type equation

2018 ◽  
Vol 11 (4) ◽  
pp. 691-705 ◽  
Author(s):  
Mudassar Imran ◽  
◽  
Youssef Raffoul ◽  
Muhammad Usman ◽  
Chi Zhang ◽  
...  
Keyword(s):  
Type Equation ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
De Vries

scholarly journals Infiltration in porous media with dynamic capillary pressure: travelling waves

2000 ◽  
Vol 11 (4) ◽  
pp. 381-397 ◽  
Author(s):  
C. CUESTA ◽  
C. J. van DUIJN ◽  
J. HULSHOF
Keyword(s):  
Porous Media ◽  
Groundwater Flow ◽  
Travelling Waves ◽  
Saturation Pressure ◽  
Type Equation ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Convective Term ◽  
Wave Solutions ◽  
Rigorous Study

We consider a model for non-static groundwater flow where the saturation-pressure relation is extended by a dynamic term. This approach, together with a convective term due to gravity, results in a pseudo-parabolic Burgers type equation. We give a rigorous study of global travelling-wave solutions, with emphasis on the role played by the dynamic term and the appearance of fronts.

scholarly journals A Mathematical Model for the Propagation of an Animal Species on a Plain

2017 ◽  
Vol 3 (2) ◽  
Author(s):  
Joel Nimyel Ndam ◽  
Stephen Dung
Keyword(s):  
Mathematical Model ◽  
Diffusion Coefficient ◽  
Animal Species ◽  
Travelling Wave ◽  
Basins Of Attraction ◽  
Travelling Wave Solutions ◽  
Density Dependent ◽  
Constant Diffusion Coefficient ◽  
Wave Solutions ◽  
Constant Diffusion

A mathematical model for the dynamics of an animal species propagating on a plain is constructed. Travelling wave solutions are then sought for two cases, the case with constant diffusion coefficient and that with density-dependent diffusion coefficient. The results show the existence of travelling wave solutions in both cases. The existence of travelling wave solutions for the two-dimensional model is important as it captures more realistically the physical interactions of species in a habitat. The minimum wave speeds as well as the basins of attraction were determined. The results also indicate the occurrence of a saddle-node bifurcation in the case with density-dependent diffusion coefficient. The basins of attraction in both cases are functions of the wave speed  and is still a subject for further investigation.

scholarly journals Existence and Orbital Stability of Cnoidal Waves for a 1D Boussinesq Equation

2007 ◽  
Vol 2007 ◽  
pp. 1-36 ◽  
Author(s):  
Jaime Angulo ◽  
Jose R. Quintero
Keyword(s):  
Orbital Stability ◽  
Type Equation ◽  
Elliptic Functions ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Jacobian Elliptic Functions ◽  
Wave Solutions ◽  
Periodic Travelling Wave ◽  
Complete Study ◽  
Set Up

We will study the existence and stability of periodic travelling-wave solutions of the nonlinear one-dimensional Boussinesq-type equationΦtt−Φxx+aΦxxxx−bΦxxtt+ΦtΦxx+2ΦxΦxt=0. Periodic travelling-wave solutions with an arbitrary fundamental periodT0will be built by using Jacobian elliptic functions. Stability (orbital) of these solutions by periodic disturbances with periodT0will be a consequence of the general stability criteria given by M. Grillakis, J. Shatah, and W. Strauss. A complete study of the periodic eigenvalue problem associated to the Lame equation is set up.

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