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.
Gevrey regularizing effect for the (generalized) Korteweg-de Vries equation and nonlinear Schrödinger equations
Global attraction to solitary waves for Klein-Gordon equation with mean field interaction
Global attractor and finite dimensionally for a class of dissipative equations of BBM's type.
Global attractor for the generalized dissipative KdV equation with nonlinearity.
Global attractor for the lattice dynamical system of a nonlinear Boussinesq equation.
Global existence and blow-up for a shallow water equation
Global existence and decay of solutions of a coupled system of BBM-Burgers equations.
The global well-posedness of the initial-value problem associated to the coupled system of BBM-Burgers equations (*) in the classical Sobolev spaces Hs(R) x Hs(R) for s ≥ 2 is studied. Furthermore we find decay estimates of the solutions of (*) in the norm Lq(R) x Lq(R), 2 ≤ q ≤ ∞ for general initial data. Model (*) is motivated by a work due to Gear and Grimshaw [10] who considered strong interaction of weakly nonlinear long waves governed by a coupled system of KdV equations.
Global solution for the Kadomtsev-Petviashvili equation (KPII) in anisotropic Sobolev spaces of negative indices.
Global well-posedness for KdV in Sobolev spaces of negative index.