Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1708238 | Applied Mathematics Letters | 2013 | 5 Pages |
Abstract
In this letter we describe how to compute the finite-genus solutions of the Korteweg-de Vries equation using a Riemann-Hilbert problem that is satisfied by the Baker-Akhiezer function corresponding to a Schrödinger operator with finite-gap spectrum. The recovery of the corresponding finite-genus solution is performed using the asymptotics of the Baker-Akhiezer function. This method has the benefit that the space and time dependence of the Baker-Akhiezer function appear in an explicit, linear and computable way. We make use of recent advances in the numerical solution of Riemann-Hilbert problems to produce an efficient and uniformly accurate numerical method for computing all finite-genus solutions of the KdV equation.
Related Topics
Physical Sciences and Engineering
Engineering
Computational Mechanics
Authors
Thomas Trogdon, Bernard Deconinck,