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Teoreticheskaya i Matematicheskaya Fizika, 1994, Volume 99, Number 2, Pages 185–200 (Mi tmf1577)  

This article is cited in 17 scientific papers (total in 17 papers)

Some new methods and results in the theory of (2+1)-dimensional integrable equations

M. Boitia, F. Pempinellia, A. K. Pogrebkovb

a Lecce University
b Steklov Mathematical Institute, Russian Academy of Sciences
References:
Abstract: The general resolvent scheme for solving nonlinear integrable evolution equations is formulated. Special attention is paid for the problem of nontrivial dressing and corresponding transformation of spectral data. Kadomtsev–Petviashvili equation is considered as the standard example of integrable models in 2+1 dimensions. Properties of the solution u(t,x,y) of the Kadomtsev–Petviashvili I equation as well as corresponding Jost solutions and spectral data with given initial data u(0,x,y) belonging to the Schwartz space are presented.
English version:
Theoretical and Mathematical Physics, 1994, Volume 99, Issue 2, Pages 511–522
DOI: https://doi.org/10.1007/BF01016132
Bibliographic databases:
Document Type: Article
Language: English
Citation: M. Boiti, F. Pempinelli, A. K. Pogrebkov, “Some new methods and results in the theory of (2+1)-dimensional integrable equations”, TMF, 99:2 (1994), 185–200; Theoret. and Math. Phys., 99:2 (1994), 511–522
Citation in format AMSBIB
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\paper Some new methods and results in the theory of ($2+1$)-dimensional integrable equations
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\issue 2
\pages 185--200
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\transl
\jour Theoret. and Math. Phys.
\yr 1994
\vol 99
\issue 2
\pages 511--522
\crossref{https://doi.org/10.1007/BF01016132}
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Linking options:
  • https://www.mathnet.ru/eng/tmf1577
  • https://www.mathnet.ru/eng/tmf/v99/i2/p185
  • This publication is cited in the following 17 articles:
    1. Ion Bica, Randy Wanye K, “Modeling rogue waves with the Kadomtsev–Petviashvili (KP) equation”, Rocky Mountain J. Math., 48:5 (2018)  crossref
    2. Boiti, M, “Scattering transform for nonstationary Schrodinger equation with bidimensionally perturbed N-soliton potential”, Journal of Mathematical Physics, 47:12 (2006), 123510  crossref  mathscinet  zmath  adsnasa  isi
    3. Boiti, M, “On the extended resolvent of the nonstationary Schrodinger operator for a Darboux transformed potential”, Journal of Physics A-Mathematical and General, 39:8 (2006), 1877  crossref  mathscinet  zmath  adsnasa  isi
    4. M. Boiti, F. Pempinelli, A. K. Pogrebkov, B. Prinari, “Spectral Theory of the Nonstationary Schrödinger Equation with a Bidimensionally Perturbed One-Dimensional Potential”, Proc. Steklov Inst. Math., 251 (2005), 6–48  mathnet  mathscinet  zmath
    5. M. Boiti, F. Pempinelli, A. K. Pogrebkov, B. Prinari, “Spectral Theory of the Nonstationary Schrodinger Equation with a Two-Dimensionally Perturbed Arbitrary One-Dimensional Potential”, Theoret. and Math. Phys., 144:2 (2005), 1100–1116  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. Boiti, M, “Extended resolvent and inverse scattering with an application to KPI”, Journal of Mathematical Physics, 44:8 (2003), 3309  crossref  mathscinet  zmath  adsnasa  isi
    7. Boiti, M, “Towards an inverse scattering theory for non-decaying potentials of the heat equation”, Inverse Problems, 17:4 (2001), 937  crossref  mathscinet  zmath  adsnasa  isi
    8. Prinari, B, “On some nondecaying potentials and related Jost solutions for the heat conduction equation”, Inverse Problems, 16:3 (2000), 589  crossref  mathscinet  zmath  adsnasa  isi
    9. A. K. Pogrebkov, M. C. Prati, “An Ablowitz–Ladik system with a discrete potential: I. Extended resolvent”, Theoret. and Math. Phys., 119:1 (1999), 407–419  mathnet  crossref  crossref  mathscinet  zmath  isi
    10. M. Boiti, F. Pempinelli, A. K. Pogrebkov, B. Prinari, “Bäcklund and Darboux Transformations for the Nonstationary Schrödinger Equation”, Proc. Steklov Inst. Math., 226 (1999), 42–62  mathnet  mathscinet  zmath
    11. M. Boiti, F. Pempinelli, A. K. Pogrebkov, B. Prinari, “Towards an inverse scattering theory for two-dimensional nondecaying potentials”, Theoret. and Math. Phys., 116:1 (1998), 741–781  mathnet  mathnet  crossref  crossref  isi
    12. M Boiti, F Pempinelli, A Pogrebkov, “Solving the Kadomtsev - Petviashvili equation with initial data not vanishing at large distances”, Inverse Problems, 13:3 (1997), L7  crossref
    13. A. K. Pogrebkov, T. I. Garagash, “On a solution of the Cauchy problem for the Boiti–Leon–Pempinelli equation”, Theoret. and Math. Phys., 109:2 (1996), 1369–1378  mathnet  crossref  crossref  mathscinet  zmath  isi
    14. A. K. Pogrebkov, M. C. Prati, “Resolvent approach to the ablowitz-ladik linear system”, Nuovo Cim B, 111:12 (1996), 1495  crossref
    15. T. I. Garagash, A. K. Pogrebkov, “Scattering problem for the differential operator xy+1+a(x,y)y+b(x,y)”, Theoret. and Math. Phys., 102:2 (1995), 117–132  mathnet  crossref  mathscinet  zmath  isi
    16. M. Boiti, F. Pempinelli, A. Pogrebkov, “Dressing of a two-dimensional nontrivial potential”, Physica D: Nonlinear Phenomena, 87:1-4 (1995), 123  crossref
    17. Theoret. and Math. Phys., 99:2 (1994), 583–587  mathnet  crossref  mathscinet  zmath  isi
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