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Teoreticheskaya i Matematicheskaya Fizika, 2005, Volume 144, Number 3, Pages 453–471
DOI: https://doi.org/10.4213/tmf1870
(Mi tmf1870)
 

This article is cited in 7 scientific papers (total in 7 papers)

The Riemann Problem and Matrix-Valued Potentials with a Convergent Baker–Akhiezer Function

A. V. Domrin

M. V. Lomonosov Moscow State University
Full-text PDF (337 kB) Citations (7)
References:
Abstract: We obtain a simple sufficient condition for the solvability of the Riemann factorization problem for matrix-valued functions on a circle. This condition is based on the symmetry principle. As an application, we consider nonlinear evolution equations that can be obtained by a unitary reduction from the zero-curvature equations connecting a linear function of the spectral parameter zz and a polynomial of zz. We consider solutions obtained by dressing the zero solution with a function holomorphic at infinity. We show that all such solutions are meromorphic functions on C2xt without singularities on R2xt. This class of solutions contains all generic finite-gap solutions and many rapidly decreasing solutions but is not exhausted by them. Any solution of this class, regarded as a function of x for almost every fixed tC, is a potential with a convergent Baker–Akhiezer function for the corresponding matrix-valued differential operator of the first order.
Keywords: Riemann factorization problem, zero-curvature conditions.
Received: 17.01.2005
English version:
Theoretical and Mathematical Physics, 2005, Volume 144, Issue 3, Pages 1264–1278
DOI: https://doi.org/10.1007/s11232-005-0158-y
Bibliographic databases:
Language: Russian
Citation: A. V. Domrin, “The Riemann Problem and Matrix-Valued Potentials with a Convergent Baker–Akhiezer Function”, TMF, 144:3 (2005), 453–471; Theoret. and Math. Phys., 144:3 (2005), 1264–1278
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/tmf1870
  • https://doi.org/10.4213/tmf1870
  • https://www.mathnet.ru/eng/tmf/v144/i3/p453
  • This publication is cited in the following 7 articles:
    1. A. V. Domrin, “Holomorphic solutions of soliton equations”, Trans. Moscow Math. Soc., 82 (2021), 193–258  mathnet  crossref
    2. Domrin A.V., “Local Inverse Scattering”, Geometric Methods in Physics, Trends in Mathematics, eds. Kielanowski P., Ali S., Bieliavsky P., Odzijewicz A., Schlichenmaier M., Voronov T., Springer Int Publishing Ag, 2016, 193–212  crossref  mathscinet  zmath  isi
    3. A. V. Domrin, “Real-analytic solutions of the nonlinear Schrödinger equation”, Trans. Moscow Math. Soc., 75 (2014), 173–183  mathnet  crossref  elib
    4. A. V. Domrin, “On holomorphic solutions of equations of Korteweg–de Vries type”, Trans. Moscow Math. Soc., 73 (2012), 193–206  mathnet  crossref  mathscinet  zmath  elib
    5. A. V. Domrin, “Meromorphic extension of solutions of soliton equations”, Izv. Math., 74:3 (2010), 461–480  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. Domrin, AV, “Local holomorphic Cauchy problem for soliton equations of parabolic type”, Doklady Mathematics, 77:3 (2008), 332  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    7. A. V. Domrin, “Remarks on the Local Version of the Inverse Scattering Method”, Proc. Steklov Inst. Math., 253 (2006), 37–50  mathnet  crossref  mathscinet  zmath
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:102
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