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 Tr. Mat. Inst. Steklova, 2006, Volume 253, Pages 46–60 (Mi tm82)

Remarks on the Local Version of the Inverse Scattering Method

A. V. Domrin

M. V. Lomonosov Moscow State University

Abstract: It is very likely that all local holomorphic solutions of integrable $(1+1)$-dimensional parabolic-type evolution equations can be obtained from the zero solution by formal gauge transformations that belong (as formal power series) to appropriate Gevrey classes. We describe in detail the construction of solutions by means of convergent gauge transformations and prove an assertion converse to the above conjecture; namely, we suggest a simple necessary condition for the existence of a local holomorphic solution to the Cauchy problem for the evolution equations under consideration in terms of scattering data of initial conditions.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2006, 253, 37–50

Bibliographic databases:

UDC: 517.958

Citation: A. V. Domrin, “Remarks on the Local Version of the Inverse Scattering Method”, Complex analysis and applications, Collected papers, Tr. Mat. Inst. Steklova, 253, Nauka, MAIK «Nauka/Inteperiodika», M., 2006, 46–60; Proc. Steklov Inst. Math., 253 (2006), 37–50

Citation in format AMSBIB
\Bibitem{Dom06} \by A.~V.~Domrin \paper Remarks on the Local Version of the Inverse Scattering Method \inbook Complex analysis and applications \bookinfo Collected papers \serial Tr. Mat. Inst. Steklova \yr 2006 \vol 253 \pages 46--60 \publ Nauka, MAIK «Nauka/Inteperiodika» \publaddr M. \mathnet{http://mi.mathnet.ru/tm82} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2338686} \transl \jour Proc. Steklov Inst. Math. \yr 2006 \vol 253 \pages 37--50 \crossref{https://doi.org/10.1134/S0081543806020040} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33748328040} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. A. V. Domrin, A. V. Domrina, “On the divergence of the Kontsevich–Witten series”, Russian Math. Surveys, 63:4 (2008), 773–775
2. A. V. Komlov, “Estimates of the Gevrey classes of scattering data for polynomial potentials”, Russian Math. Surveys, 63:4 (2008), 788–789
3. A. V. Domrin, “Meromorphic extension of solutions of soliton equations”, Izv. Math., 74:3 (2010), 461–480
4. A. V. Domrin, “On holomorphic solutions of equations of Korteweg–de Vries type”, Trans. Moscow Math. Soc., 73 (2012), 193–206
5. A. V. Domrin, “Real-analytic solutions of the nonlinear Schrödinger equation”, Trans. Moscow Math. Soc., 75 (2014), 173–183
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