Related papers: KdV equation under periodic boundary conditions an…
We investigate the ultradiscrete KdV equation with periodic boundary conditions where the two parameters (capacity of the boxes and that of the carrier) are arbitrary integers. We give a criterion to allow a periodic boundary condition when…
Near linear evolution in Korteweg de Vries (KdV) equation with periodic boundary conditions is established under the assumption of high frequency initial data. This result is obtained by the method of normal form reduction.
This paper is concerned with a class of partial differential equations, which are the linear combinations, with constant coefficients, of the classical flows of the KdV hierarchy. A boundary value problem with inhomogeneous boundary…
Dispersive averaging effects are used to show that KdV equation with periodic boundary conditions possesses high frequency solutions which behave nearly linearly. Numerical simulations are presented which indicate high accuracy of this…
We prove local in time well-posedness for a class of quasilinear Hamiltonian KdV-type equations with periodic boundary conditions, more precisely we show existence, uniqueness and continuity of the solution map. We improve the previous…
In this paper, the complex version KdV equation is discussed. The corresponding coupled equations is a integrable system in the sense of the bi-Hamiltonian structure, so the complex version KdV equation is integrable. A new spectral form is…
The method for solving the KdV are considered.
In this paper the stability of the Korteweg-de Vries (KdV) equation is investigated. It is shown analytically and numerically that small perturbations of solutions of the KdV-equation introduce effects of dispersion, hence the perturbation…
A forced KdV equation is derived to describe weakly nonlinear, shallow water surface wave propagation over non trivial bottom boundary condition. We show that different functional forms of bottom boundary conditions self-consistently…
We consider the KdV equation on the Sobolev space of periodic distributions. We obtain estimates of the solution of the KdV in terms of action variables.
An initial-boundary value problem for a generalized KdV equation posed on a half-line is considered. Existence and uniqueness of global regular solutions for arbitrary smooth initial data are established.
The work presented here emanates from questions arising from experimental observations of the propagation of surface water waves. The experiments in question featured a periodically moving wavemaker located at one end of a flume that…
The KdV equation is a model equation for waves at the surface of an inviscid incompressible fluid, and it is well known that the equation describes the evolution of unidirectional waves of small amplitude and long wavelength fairly…
We are interested in the description of small modulations in time and space of wave-train solutions to the complex Ginzburg-Landau equation \begin{align*} \partial_T \Psi = (1+ i \alpha) \partial_X^2 \Psi + \Psi - (1+i \beta ) \Psi…
We study the existence and stability of periodic traveling-wave solutions for complex modified Korteweg-de Vries equation. We also discuss the problem of uniform continuity of the data-solution mapping.
This paper is concerned with the boundary-value problem on the Boltzmann equation in bounded domains with diffuse-reflection boundary where the boundary temperature is time-periodic. We establish the existence of time-periodic solutions…
Stationary solutions on a bounded interval for an initial-boundary value problem to Korteweg--de~Vries and modified Korteweg--de~Vries equation (for the last one both in focusing and defocusing cases) are constructed. The method of the…
We prove the nonlinear stability of the KdV solitary waves considered as solutions of the KP-II equation, with respect to periodic transverse perturbations.
For the KdV-Burgers equations for cylindrical and spherical waves the development of a regular profile starting from an equilibrium under a periodic perturbation at the boundary is studied. The equation describes a medium which is both…
In this article, we study an initial-boundary-value problem of a coupled KdV-KdV system on the half line $ \mathbb{R}^+ $ with non-homogeneous boundary conditions: \begin{equation*} \left\{ \begin{array}{l} u_t+v_x+u u_x+v_{xxx}=0, \quad…