A Riemann-Hilbert Approach for the Novikov Equation

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2016
• ISSN: 1815-0659
• Main Authors: Boutet de Monvel, A., Shepelsky, D., Zielinski, L.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2016
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/147860
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: A Riemann-Hilbert Approach for the Novikov Equation / A. Boutet de Monvel, D. Shepelsky, L. Zielinski // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 44 назв. — англ.

We develop the inverse scattering transform method for the Novikov equation ut−utxx+4u²ux=3uuxuxx+u²uxxx considered on the line x∈(−∞,∞) in the case of non-zero constant background. The approach is based on the analysis of an associated Riemann-Hilbert (RH) problem, which in this case is a 3×3 matri...