A Riemann-Hilbert approach for the Degasperis-Procesi equation

2011/07/29 by Anne Boutet de Monvel, Dmitry Shepelsky, de Monvel, A. Boutet +1 · 4 citations
Computer Science · Mathematics · #35B40 #35Q15 #35Q51 #35Q53 (Primary) 37K15 #37K40 (Secondary) #Advanced Mathematical Modeling in Engineering #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1107.5995

openalex publication_date 2011/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present an inverse scattering transform approach to the Cauchy problem on the line for the Degasperis--Procesi equation u_t-u_txx+3ωu_x+4uu_x=3u_xu_xx+uu_xxx in the form of an associated Riemann-Hilbert problem. This approach allows us to give a representation of the solution to the Cauchy problem, which can be efficiently used in studying its long-time behavior.

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• The Nonlinear Steepest Descent Method to Long-Time Asymptotics of the Coupled Nonlinear Schrödinger Equation
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