Discretization of Camassa-Holm peakon equation using orthogonal polynomials and matrix $LR$ transformations

Author:

R. Watanabe, M. Iwasaki, S. Tsujimoto

Keyword:

Nonlinear Sciences, Exactly Solvable and Integrable Systems, Exactly Solvable and Integrable Systems (nlin.SI), Dynamical Systems (math.DS)

journal:

date:

2023-11-28 00:00:00

Abstract

Discrete integrable systems are closely related to orthogonal polynomials and isospectral matrix transformations. In this paper, we use these relationships to propose a nonautonomous time-discretization of the Camassa-Holm (CH) peakon equation, which describes the motion of peakon waves, which are soliton waves with sharp peaks. We then validate our time-discretization, and clarify its asymptotic behavior as the discrete-time goes to infinity. We present numerical examples to demonstrate that the proposed discrete equation captures peakon wave motions.

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