Modulated traveling fronts for a nonlocal Fisher-KPP equation: a dynamical systems approach

@article{Faye2014ModulatedTF,
  title={Modulated traveling fronts for a nonlocal Fisher-KPP equation: a dynamical systems approach},
  author={Gr{\'e}gory Faye and Matt Holzer},
  journal={arXiv: Analysis of PDEs},
  year={2014}
}

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References

SHOWING 1-10 OF 35 REFERENCES
Wave-like Solutions for Nonlocal Reaction-diffusion Equations: a Toy Model
Traveling waves for the nonlocal Fisher Equation can exhibit much more complex behaviours than for the usual Fisher equation. A striking numerical observation is that a traveling wave with minimal
The non-local Fisher-KPP equation: travelling waves and steady states
We consider the Fisher–KPP equation with a non-local saturation effect defined through an interaction kernel ϕ(x) and investigate the possible differences with the standard Fisher–KPP equation. Our
Travelling front solutions of a nonlocal Fisher equation
TLDR
This work considers a scalar reaction-diffusion equation containing a nonlocal term (an integral convolution in space) of which Fisher’s equation is a particular case and shows that if the nonlocality is sufficiently weak in a certain sense then such travelling fronts exist.
Bifurcating fronts for the Taylor-Couette problem in infinite cylinders
We show the existence of bifurcating fronts for the weakly unstable Taylor—Couette problem in an infinite cylinder. These fronts connect a stationary bifurcating pattern, here the Taylor vortices,
Spatial structures and generalized travelling waves for an integro-differential equation
Some models in population dynamics with intra-specific competition lead to integro-differential equations where the integral term corresponds to nonlocal consumption of resources [8][9]. The
On the nonlocal Fisher-KPP equation: steady states, spreading speed and global bounds
We consider the Fisher–KPP (for Kolmogorov–Petrovsky–Piskunov) equation with a nonlocal interaction term. We establish a condition on the interaction that allows for existence of non-constant
Non-linear wave-number interaction in near-critical two-dimensional flows
This paper deals with a system of equations which includes as special cases the equations governing such hydrodynamic stability problems as the Taylor problem, the Bénard problem, and the stability
Instabilities and fronts in extended systems
The physics of extended systems is a topic of great interest for the experimentalist and the theoretician alike. There exists a large literature on this subject in which solutions, bifurcations,
...
...