Distributed control of the generalized Korteweg-de Vries-Burgers equation.
Dubrovin Type Equations for Completely Integrable Systems Associated with a Polynomial Pencil
Dubrovin type equations for the N -gap solution of a completely integrable system associated with a polynomial pencil is constructed and then integrated to a system of functional equations. The approach used to derive those results is a generalization of the familiar process of finding the 1-soliton (1-gap) solution by integrating the ODE obtained from the soliton equation via the substitution u = u(x + λt).
Dynamics of a modified Davey-Stewartson system in ℝ³
We study the Cauchy problem in ℝ³ for the modified Davey-Stewartson system , . Under certain conditions on λ₁ and λ₂, we provide a complete picture of the local and global well-posedness, scattering and blow-up of the solutions in the energy space. Methods used in the paper are based upon the perturbation theory from [Tao et al., Comm. Partial Differential Equations 32 (2007), 1281-1343] and the convexity method from [Glassey, J. Math. Phys. 18 (1977), 1794-1797].
Elements of a qualitative theory of Hamiltonian PDEs.
Équation de Burgers avec conditions initiales à accroissements indépendants et homogènes
Erratum to : “Existence globale et comportement asymptotique pour l'équation de Klein–Gordon quasi linéaire à données petites en dimension 1”
Error estimate for a fully discrete spectral scheme for Korteweg-de Vries-Kawahara equation
We are concerned with convergence of spectral method for the numerical solution of the initial-boundary value problem associated to the Korteweg-de Vries-Kawahara equation (Kawahara equation, in short), which is a transport equation perturbed by dispersive terms of the 3rd and 5th order. This equation appears in several fluid dynamics problems. It describes the evolution of small but finite amplitude long waves in various problems in fluid dynamics. These equations are discretized in space by the...
Exact boundary controllability of a nonlinear KdV equation with critical lengths
We study the boundary controllability of a nonlinear Korteweg–de Vries equation with the Dirichlet boundary condition on an interval with a critical length for which it has been shown by Rosier that the linearized control system around the origin is not controllable. We prove that the nonlinear term gives the local controllability around the origin.
Exact solutions and localized structures for higher-dimensional Burgers systems.
Exact solutions for a new fifth-order integrable system.
Exact solutions for a third-order KdV equation with variable coefficients and forcing term.
Exact solutions for the generalized BBM equation with variable coefficients.
Exact solutions of the generalized Benjamin-Bona-Mahony equation.
Exact solutions to KdV6 equation by using a new approach of the projective Riccati equation method.
Existence and analyticity of lump solutions for generalized Benney-Luke equations.
Existence and orbital stability of cnoidal waves for a 1D Boussinesq equation.
Existence and uniqueness for a nonlinear dispersive equation.
Existence and uniqueness of a periodic solution to the two-dimensional generalized Korteweg-de Vries equation
Existence globale et comportement asymptotique pour l'équation de Klein–Gordon quasi linéaire à données petites en dimension 1
Existence of periodic traveling wave solution to the forced generalized nearly concentric Korteweg-de Vries equation.