Existence of periodic traveling wave solutions to the generalized forced Boussinesq equation.
Existence of solutions to nonlinear advection-diffusion equation applied to Burgers' equation using Sinc methods
This paper has two objectives. First, we prove the existence of solutions to the general advection-diffusion equation subject to a reasonably smooth initial condition. We investigate the behavior of the solution of these problems for large values of time. Secondly, a numerical scheme using the Sinc-Galerkin method is developed to approximate the solution of a simple model of turbulence, which is a special case of the advection-diffusion equation, known as Burgers' equation. The approximate solution...
Existence of solutions to the Rosenau and Benjamin-Bona-Mahony equation in domains with moving boundary.
Explicit solutions of generalized nonlinear Boussinesq equations.
Exponential convergence to the stationary measure and hyperbolicity of the minimisers for random Lagrangian Systems
We consider a class of 1d Lagrangian systems with random forcing in the spaceperiodic setting: These systems have been studied since the 1990s by Khanin, Sinai and their collaborators [7, 9, 11, 12, 15]. Here we give an overview of their results and then we expose our recent proof of the exponential convergence to the stationary measure [6]. This is the first such result in a classical setting, i.e. in the dual-Lipschitz metric with respect to the Lebesgue space for finite , partially answering...
Exponentially slow traveling waves on a finite interval for Burger's type equation.
Fourth order time-stepping for low dispersion Korteweg-de Vries and nonlinear Schrödinger equations.
Fredholm determinants
The article provides with a down to earth exposition of the Fredholm theory with applications to Brownian motion and KdV equation.
Further extended sinh-cosh and sin-cos methods and new nontraveling wave solutions of the -dimensional dispersive long wave equations.
Gain of regularity for a Korteweg-de Vries--Kawahara type equation.
Gain of regularity for equations of KdV type
Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation
Inspired by the work of Zhidkov on the KdV equation, we perform a construction of weighted Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation. The resulting measures are supported by Sobolev spaces of increasing regularity. We also prove a property on the support of these measures leading to the conjecture that they are indeed invariant by the flow of the Benjamin-Ono equation.
General mixed problems for the KdV equations on bounded intervals.
Generalized Jacobi elliptic function solution to a class of nonlinear Schrödinger-type equations.
Generalized solutions to the gKdV equation.
Geodesic flow and two (super) component analog of the Camassa-Holm equation.
Geometric realizations of bi-Hamiltonian completely integrable systems.
Geometrical methods in hydrodynamics
We describe some recent results on a specific nonlinear hydrodynamical problem where the geometric approach gives insight into a variety of aspects.
Geometry and analytic theory of Frobenius manifolds.
Geometry of KDV(4): Abel sums, Jacobi variety, and theta function in the scattering case.