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This course was given at ENSET Oran, November 4-9, 2006. It is
an introduction to isometric actions of Lie groups on Lorentz manifolds.
Several examples are presented, followed by general defi...
Analysis of a Non-linear Partial Difference Equation, and Its Application to Cardiac Dynamics
Partial difference equation Non-linear Cardiac dynamics Singular perturbation method Spatial bifurcations
2015/8/27
A model of a strip of cardiac tissue consisting of a one-dimensional chain of cardiac units is derived in the form of a non-linear partial difference equation. Perturbation analysis is performed on th...
Nonlinear Dynamics and Chaos: Where do we go from here?
Dynamics and Chaos Colston conference
2015/8/25
In keeping with the spirit of the Colston conference on Nonlinear Dynam-
ics and Chaos, this chapter emphasizes ideas more than details, describing
my vision of how the bifurcation theory of multipl...
Existence, Stability, and Dynamics of Solitary Waves in Nonlinear Schroedinger Models with Periodic Potentials
Non-square lattices, Nonlinear waves Photonic lattices
2014/12/8
The focus of this dissertation is the existence, stability, and resulting dynamical evolution of localized stationary solutions to Nonlinear Schr¨odinger (NLS) equations with periodic confining potent...
Local Dynamics Near Unstable Branches of NLS Solitons
Local Dynamics Unstable Branches of NLS Solitons Analysis of PDEs
2012/7/11
Consider a branch of unstable solitons of NLS whose linearized operators have one pair of simple real eigenvalues in addition to the zero eigenvalue. Under radial symmetry and standard assumptions, so...
Soliton dynamics of NLS with singular potentials
Nonlinear Schrodinger equation soliton dynamics singular potentials
2012/6/30
We investigate the validity of a soliton dynamics behavior in the semi-relativistic limit for the nonlinear Schr\"odinger equation in $\R^{N}, N\ge 3$, in presence of a singular external potential.
Long-time dynamics of the parabolic $p$-Laplacian equation
p-Laplacian equation attractors Long-time dynamics
2012/2/29
In this paper, we study the long-time behaviour of solutions of Cauchy problem for the parabolic $p$-Laplacian equation with variable coefficients. Under mild conditions on the coefficient of the prin...
Interface dynamics of the porous medium equation with a bistable reaction term
degenerate diffusion singular perturbation sharp interface limit population dynamics
2011/9/14
Abstract: We consider a degenerate partial differential equation arising in population dynamics, namely the porous medium equation with a bistable reaction term. We study its asymptotic behavior as a ...
On the Production of Dissipation by Interaction of Forced Oscillating Waves in Fluid Dynamics
Equations of mixed hyperbolic and parabolic type oscillations BKW Calculus stability
2011/8/25
Abstract: In the context of some bidimensionnal Navier-Stokes model, we exhibit a family of exact oscillating solutions $\{u_{\epsilon}\}_{\epsilon}$ defined on some strip $[0,T]\times\R^2$ which does...
Chemotaxis: from kinetic equations to aggregate dynamics
duality solutions non local conservation equations hydrodynamic limit measure-valued solutions chemotaxis
2011/8/25
Abstract: The hydrodynamic limit for a kinetic model of chemotaxis is investigated. The limit equation is a non local conservation law, for which finite time blow-up occurs, giving rise to measure-val...
Finite-temperature nonlinear dynamics in cavity QED: A Thermofield Dynamics Approach
cavity QED Finite-temperature nonlinear dynamics Thermofield Dynamics Approach
2011/7/7
Heath-bath effects in the dynamics of atom + cavity system are studied. The temperature effects are explored using thermofield dynamics formalism. It is found that the dynamics of the system is sensit...
The Nonlinear Schroedinger Equation: Existence, Stability and Dynamics of Solitons
Soliton dynamics Nonlinear Schroedinger Equation
2011/2/28
In this paper we present some recent results concerning the existence,the stability and the dynamics of solitons occurring in the nonlinear Schroedinger equation when the parameter h → 0.
On the abundance of non-zero central Lyapunov exponents, physical measures and stable ergodicity for partially hyperbolic dynamics
u-Gibbs states physical measures partially hyperbolic dynamics minimal foliations
2011/1/20
We show that each strongly partially hyperbolic C2 diffeomorphism, with one-dimensional subbundles and C2 smooth andminimal strong-unstable foliation, is C2 close to a diffeomorphism having non-zero c...
Effective dynamics for $N$-solitons of the Gross-Pitaevskii equation
Effective dynamics $N$-solitons Gross-Pitaevskii equation
2010/12/13
We consider several solitons moving in a slowly varying external eld. We show that the e ective dynamics obtained by restricting the full Hamiltonian to the nite dimensional manifold of N-solitons (...