The Linear KdV Equation with an Interface

Abstract

The interface problem for the linear Korteweg-de Vries (KdV) equation in one-dimensional piecewise homogeneous domains is examined by constructing an explicit solution in each domain. The location of the interface is known and a number of compatibility conditions at the boundary are imposed. We provide an explicit characterization of sufficient interface conditions for the construction of a solution using Fokas's Unified Transform Method. The problem and the method considered here extend that of earlier papers to problems with more than two spatial derivatives.

arXiv comment23 pages, 8 figures

References in corpus (6)

• A Transform Method for Evolution PDEs on a Finite Interval
• Non-steady state heat conduction in composite walls
• Heat equation on a network using the Fokas method
• Interface Problems for Dispersive equations
• Gibbs phenomenon for dispersive PDEs on the line
• Generalized Dirichlet to Neumann Maps for Linear Dispersive Equations on Half-Line

Cited by in corpus (5)

• The Korteweg-de Vries equation on a metric star graph
• Airy-type evolution equations on star graphs
• Linear Dispersive Shocks
• Boundary value problems for evolution partial differential equations with discontinuous data
• The Linearized Classical Boussinesq System on the Half-Line