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Title: Efficient computation of soliton gas primitive potentials
We consider the problem of computing a class of soliton gas primitive potentials for the Korteweg-de Vries equation that arise from the accumulation of solitons on an infinite interval in the physical domain, extending to $$-\infty$$. This accumulation results in an associated Riemann-Hilbert Problem (RHP) on a number of disjoint intervals. In the case where the jump matrices have specific square-root behaviour, we describe an efficient and accurate numerical method to solve this RHP and extract the potential. The keys to the method are, first, the deformation of the RHP, making numerical use of the so-called $$g$$-function, and, second, the incorporation of endpoint singularities into the chosen basis to discretize and solve the associated singular integral equation.  more » « less
Award ID(s):
2108029
PAR ID:
10650353
Author(s) / Creator(s):
; ;
Publisher / Repository:
Cambridge University Press
Date Published:
Journal Name:
Journal of Nonlinear Waves
Volume:
1
ISSN:
3033-4268
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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