Generalized Dirichlet to Neumann Maps for Linear Dispersive Equations on Half-Line

TL;DR

This paper develops explicit formulas for the generalized Dirichlet to Neumann maps for linear dispersive PDEs on the half-line, enabling the determination of unknown boundary data from given initial and boundary conditions using the unified transform method.

Contribution

It introduces a unified approach to explicitly compute boundary values for linear dispersive equations on the half-line, expanding the applicability of the unified transform method.

Findings

Explicit formulas for Dirichlet to Neumann maps derived

Applicable to a broad class of linear dispersive PDEs

Enhances boundary value problem solving techniques

Abstract

A large class of initial-boundary value problems of linear evolution partial differential equations formulated on the half-line is analyzed via the unified transform method. In particular, explicit formulae are presented for the generalized Dirichlet to Neumann maps. Namely, the determination of the unknown boundary values in terms of an essential set of given data.