Analytical and numerical methods for the CMKdV-II equation.
Applications of the new compound Riccati equations rational expansion method and Fan's subequation method for the Davey-Stewartson equations.
Blow up and near soliton dynamics for the critical gKdV equation
These notes present the main results of [22, 23, 24] concerning the mass critical (gKdV) equation for initial data in close to the soliton. These works revisit the blow up phenomenon close to the family of solitons in several directions: definition of the stable blow up and classification of all possible behaviors in a suitable functional setting, description of the minimal mass blow up in , construction of various exotic blow up rates in , including grow up in infinite time.
Blow up for the critical gKdV equation. II: Minimal mass dynamics
We consider the mass critical (gKdV) equation for initial data in . We first prove the existence and uniqueness in the energy space of a minimal mass blow up solution and give a sharp description of the corresponding blow up soliton-like bubble. We then show that this solution is the universal attractor of all solutions near the ground state which have a defocusing behavior. This allows us to sharpen the description of near soliton dynamics obtained in [29].
Construction de solutions pour les équations de Korteweg-de Vries généralisées
Exact solutions and localized structures for higher-dimensional Burgers systems.
Exact solutions to KdV6 equation by using a new approach of the projective Riccati equation method.
-stability of multi-solitons
The aim of this note is to give a short review of our recent work (see [5]) with Miguel A. Alejo and Luis Vega, concerning the -stability, and asymptotic stability, of the -soliton of the Korteweg-de Vries (KdV) equation.
New exact solutions for the -dimensional Broer-Kaup-Kupershmidt equations.
New solitons and periodic solutions for Thekadomtsev-Petviashvili equation.
Numerical computation of soliton dynamics for NLS equations in a driving potential.
On the numerical solutions of some fractional ordinary differential equations by fractional Adams-Bashforth-Moulton method
In this paper, we apply the Fractional Adams-Bashforth-Moulton Method for obtaining the numerical solutions of some linear and nonlinear fractional ordinary differential equations. Then, we construct a table including numerical results for both fractional differential equations. Then, we draw two dimensional surfaces of numerical solutions and analytical solutions by considering the suitable values of parameters. Finally, we use the L2 nodal norm and L∞ maximum nodal norm to evaluate the accuracy...
Periodic and solitary wave solutions of two component Zakharov-Yajima-Oikawa system, using Madelung's approach.
Periodic and solitary wave solutions to the Fornberg-Whitham equation.
Riesz potentials for Korteweg-de Vries solitons and Sturm-Liouville problems.
Solitary wave solutions for a time-fraction generalized Hirota-Satsuma coupled KdV equation by a new analytical technique.
Solitary waves for a coupled nonlinear Schrödinger system with dispersion management.
Soliton dynamics for the Korteweg-de Vries equation with multiplicative homogeneous noise.
Solitons and Gibbs Measures for Nonlinear Schrödinger Equations
We review some recent results concerning Gibbs measures for nonlinear Schrödinger equations (NLS), with implications for the theory of the NLS, including stability and typicality of solitary wave structures. In particular, we discuss the Gibbs measures of the discrete NLS in three dimensions, where there is a striking phase transition to soliton-like behavior.
Stabilité des solitons de l’équation de Landau-Lifshitz à anisotropie planaire
Cet exposé présente plusieurs résultats récents quant à la stabilité des solitons sombres de l’équation de Landau-Lifshitz à anisotropie planaire, en particulier, quant à la stabilité orbitale des trains (bien préparés) de solitons gris [16] et à la stabilité asymptotique de ces mêmes solitons [2].