# The Linear KdV Equation with an Interface

@inproceedings{Deconinck2015TheLK, title={The Linear KdV Equation with an Interface}, author={Bernard Deconinck and Natalie E. Sheils and David A. Smith}, year={2015} }

- Published 2015

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… CONTINUE READING

#### From This Paper

##### Figures, tables, and topics from this paper.

#### Citations

##### Publications citing this paper.

Showing 1-4 of 4 extracted citations

## Exact boundary controllability of the Korteweg-de Vries equation with a piecewise constant main coefficient

View 3 Excerpts

Highly Influenced

#### References

##### Publications referenced by this paper.

Showing 1-10 of 24 references

## Exact solution of the Korteweg–de Vries equation for multiple collisions of solitons

View 6 Excerpts

Highly Influenced

## Korteweg-de Vries equation: A completely integrable Hamiltonian system

View 6 Excerpts

Highly Influenced

## Generalized Dirichlet to Neumann maps for linear dispersive equations on the half-line

View 5 Excerpts

Highly Influenced

## A unified approach to boundary value problems, volume 78 of CBMS-NSF Regional Conference Series in Applied Mathematics

View 8 Excerpts

Highly Influenced

## Gibbs Phenomenon for Dispersive PDEs on the Line

View 2 Excerpts

## A unified numerical approach for the Nonlinear Schrödinger Equations

View 1 Excerpt

## Heat equation on a network using the Fokas method

View 2 Excerpts

## The time-dependent Schrödinger equation with piecewise constant potentials

View 2 Excerpts

## Fokas method for a multidomain linear reaction-diffusion equation with discontinuous diffusivity

View 3 Excerpts

## Fokas transform method for a brain tumor invasion model with heterogeneous diffusion in dimensions

View 3 Excerpts