A Riemann-Hilbert Approach for the Novikov Equation
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
A Riemann-Hilbert Approach for the Novikov Equation
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| Creator |
Boutet de Monvel, A.
Shepelsky, D. Zielinski, L. |
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| Description |
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.
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| Date |
2019-02-16T09:26:42Z
2019-02-16T09:26:42Z 2016 |
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| Type |
Article
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| Identifier |
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.
1815-0659 2010 Mathematics Subject Classification: 35Q53; 37K15; 35Q15; 35B40; 35Q51; 37K40 DOI:10.3842/SIGMA.2016.095 http://dspace.nbuv.gov.ua/handle/123456789/147860 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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