The Initial-boundary Value Problem for the Ostrovsky-Vakhnenko Equation on the Half-line

  • Jian Xu
  • Engui Fan


We analyze an initial-boundary value problem for the Ostrovsky-Vakhnenko equation on the half-line. This equation can be viewed as the short wave model for the Degasperis-Procesi (DP) equation. We show that the solution u(x,t) can be recovered from its initial and boundary values via the solution of a vector Riemann-Hilbert problem formulated in the plane of a complex spectral parameter z.


Ostrovsky-Vakhnenko equation Initial-boundary value problem Riemann-Hilbert problem 

Mathematics Subject Classification (2010)

35Q15 30E25 31B20 


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.College of ScienceUniversity of Shanghai for Science and TechnologyShanghaiPeople’s Republic of China
  2. 2.School of Mathematical Sciences, Key Laboratory of Mathematics for Nonlinear ScienceFudan UniversityShanghaiPeople’s Republic of China

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