Abstract
We introduce a method of solving initial boundary value problems for linear evolution equations in a time-dependent domain, and we apply it to an equation with dispersion relation , in the domain , . We show that the solution of this problem admits an integral representation in the complex plane, involving either an integral of along a time-dependent contour, or an integral of over a fixed two-dimensional domain. The functions and can be computed through the solution of a system of Volterra linear integral equations. This method can be generalized to nonlinear integrable partial differential equations.
- Received 12 May 1999
DOI:https://doi.org/10.1103/PhysRevLett.84.4785
©2000 American Physical Society