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.
Global well-posedness of NLS-KdV systems for periodic functions.
Global well-posedness of the initial value problem for the Hirota-Satsuma system.
Hamiltonian flows of curves in and vector soliton equations of mKdV and sine-Gordon type.
Hamiltonian structure and new exact soliton solutions of some Korteweg--de Vries equations.
Hermite pseudospectral method for nonlinear partial differential equations
Hermite pseudospectral method for nonlinear partial differential equations
Hermite polynomial interpolation is investigated. Some approximation results are obtained. As an example, the Burgers equation on the whole line is considered. The stability and the convergence of proposed Hermite pseudospectral scheme are proved strictly. Numerical results are presented.
Higher-order equations of the KdV type are integrable.
Higher-order KdV-type equations and their stability.
Holomorphic solution for classes of forced Korteweg-de Vries equations of fractional order
Implicit difference scheme for the numerical resolution of the Charney-Obukhov equation with variable coefficients.