A Riemann-Hilbert Approach for the Novikov Equation
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...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2016 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2016
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147860 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862742532028366848 |
|---|---|
| author | Boutet de Monvel, A. Shepelsky, D. Zielinski, L. |
| author_facet | Boutet de Monvel, A. Shepelsky, D. Zielinski, L. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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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| first_indexed | 2025-12-07T20:25:35Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147860 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T20:25:35Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Boutet de Monvel, A. Shepelsky, D. Zielinski, L. 2019-02-16T09:26:42Z 2019-02-16T09:26:42Z 2016 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 https://nasplib.isofts.kiev.ua/handle/123456789/147860 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Riemann-Hilbert Approach for the Novikov Equation Article published earlier |
| spellingShingle | A Riemann-Hilbert Approach for the Novikov Equation Boutet de Monvel, A. Shepelsky, D. Zielinski, L. |
| title | A Riemann-Hilbert Approach for the Novikov Equation |
| title_full | A Riemann-Hilbert Approach for the Novikov Equation |
| title_fullStr | A Riemann-Hilbert Approach for the Novikov Equation |
| title_full_unstemmed | A Riemann-Hilbert Approach for the Novikov Equation |
| title_short | A Riemann-Hilbert Approach for the Novikov Equation |
| title_sort | riemann-hilbert approach for the novikov equation |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147860 |
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