Papers › Efficient computation of soliton gas primitive potentials
Efficient computation of soliton gas primitive potentials
Cade Ballew, Deniz Bilman, Thomas Trogdon
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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 -∞. This accumulation results in an associated Riemann--Hilbert problem on a number of disjoint intervals. In the case where the jump matrices have specific square-root behavior, we describe an efficient and accurate numerical method to solve this Riemann--Hilbert problem and extract the potential. The keys to the method are, first, the deformation of the Riemann--Hilbert problem, 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.
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