The Ostrovsky-Vakhnenko equation by a Riemann-Hilbert approach

2013/11/03 by de Monvel, Anne Boutet, Shepelsky, Dmitry
#35B40 #35Q15 #35Q51 #35Q53 (Primary) 37K15 #37K40 (Secondary) #Analysis of PDEs (math.AP) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1311.0495

Abstract

We present an inverse scattering transform approach for the equation u_txx-3u_x+3u_xu_xx+uu_xxx=0. This equation can be viewed as the short wave model for the Degasperis-Procesi equation or the differentiated Ostrovsky-Vakhnenko equation. The approach is based on an associated Riemann-Hilbert problem, which allows us to give a representation for the classical (smooth) solution, to get the principal term of its long time asymptotics, and also to describe loop soliton solutions.

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