A Riemann-Hilbert Approach for the Novikov Equation

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Фізико-технічні та математичні науки
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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12
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Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12, випуск за цей рік
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dc.contributor.author	Boutet de Monvel, A.
dc.contributor.author	Shepelsky, D.
dc.contributor.author	Zielinski, L.
dc.date.accessioned	2019-02-16T09:26:42Z
dc.date.available	2019-02-16T09:26:42Z
dc.date.issued	2016
dc.identifier.citation	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.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 35Q53; 37K15; 35Q15; 35B40; 35Q51; 37K40
dc.identifier.other	DOI:10.3842/SIGMA.2016.095
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/147860
dc.description.abstract	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 matrix problem. The structure of this RH problem shares many common features with the case of the Degasperis-Procesi (DP) equation having quadratic nonlinear terms (see [Boutet de Monvel A., Shepelsky D., Nonlinearity 26 (2013), 2081-2107, arXiv:1107.5995]) and thus the Novikov equation can be viewed as a ''modified DP equation'', in analogy with the relationship between the Korteweg-de Vries (KdV) equation and the modified Korteweg-de Vries (mKdV) equation. We present parametric formulas giving the solution of the Cauchy problem for the Novikov equation in terms of the solution of the RH problem and discuss the possibilities to use the developed formalism for further studying of the Novikov equation.	uk_UA
dc.description.sponsorship	This paper is a contribution to the Special Issue on Asymptotics and Universality in Random Matrices, Random Growth Processes, Integrable Systems and Statistical Physics in honor of Percy Deift and Craig Tracy. The full collection is available at http://www.emis.de/journals/SIGMA/Deift-Tracy.html.	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Інститут математики НАН України	uk_UA
dc.relation.ispartof	Symmetry, Integrability and Geometry: Methods and Applications
dc.title	A Riemann-Hilbert Approach for the Novikov Equation	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA