We study the stability/instability of the subsonic travelling waves of the Nonlinear Schrödinger Equation in dimension one. Our aim is to propose several methods for showing instability (use of the GrillakisShatah-Strauss theory, proof of existence of an unstable eigenvalue via an Evans function) or stability. For the later, we show how to construct in a systematic way a Liapounov functional fo...

In this paper we study the existence and qualitative properties of travelling waves associated to a nonlinear flux limited partial differential equation coupled to a Fisher–Kolmogorov–Petrovskii–Piskunov type reaction term. We prove the existence and uniqueness of finite speed moving fronts of C classical regularity, but also the existence of discontinuous entropy travelling wave solutions.

We consider a nonlinear system of parabolic equations describing the transport of contaminant in porous media. For this system travelling wave solutions are known to exist. We prove existence and uniqueness of general solutions of the system and convergence to travelling waves.

We describe a continuous-wave master-oscillator power-amplifier system based on a distributed Bragg reflection diode laser and an Yb doped fiber amplifier. The observed optical spectrum of the amplified seed source can be tailored to arbitrary shapes and widths between 30 MHz and greater than 1 GHz by controlling the radio frequency modulation wave form of the injection current. © 2006 American...

In this paper we present a model for crystal dissolution in porous media and we analyse travelling wave solutions of the ensuing equations for a one{dimensional ow situation. We demonstrate the structure of the waves and we prove existence and uniqueness. The travelling wave description is characterized by a rate parameter k and a diiusion/dispersion parameter D. We investigate the limit proces...

We consider a three strategy game in which a pure strategy is an evolutionarily stable strategy (ESS). The individuals are moving randomly (modelled by diffusion) in a (1-dimensional) spatial environment which is homogeneous. It is shown that, contrary to intuition, even if the ESS is spatially dominant against each of the other two strategies separately, there might be a travelling wave which ...

Recent discoveries of phosphorylation gradients and microdomains with different protein activities have revolutionized our perception of information transfer within single cells. The different spatial localization of opposing reactions in protein-modification cycles has been shown to bring about heterogeneous stationary patterns and travelling waves of protein activities. We review spatial patt...

Zufiria’s higher-order Boussinesq type equations are studied by transforming them into solvable ordinary differential equations. Various families of their travelling wave solutions are generated, which include periodic wave, solitary wave, periodic-like wave, solitonlike wave, Jacobi elliptic function periodic wave, combined non-degenerative Jacobi elliptic function-like wave, Weierstrass ellip...