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TMF, 1994, Volume 99, Number 2, Pages 185–200 (Mi tmf1577)  

This article is cited in 12 scientific papers (total in 12 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

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.

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English version:
Theoretical and Mathematical Physics, 1994, 99:2, 511–522

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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
\by M.~Boiti, F.~Pempinelli, A.~K.~Pogrebkov
\paper Some new methods and results in the theory of ($2+1$)-dimensional integrable equations
\jour TMF
\yr 1994
\vol 99
\issue 2
\pages 185--200
\jour Theoret. and Math. Phys.
\yr 1994
\vol 99
\issue 2
\pages 511--522

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    This publication is cited in the following articles:
    1. Theoret. and Math. Phys., 99:2 (1994), 583–587  mathnet  crossref  mathscinet  zmath  isi
    2. T. I. Garagash, A. K. Pogrebkov, “Scattering problem for the differential operator $\partial_x\partial_y+1+a(x,y)\partial_y+ b(x,y)$”, Theoret. and Math. Phys., 102:2 (1995), 117–132  mathnet  crossref  mathscinet  zmath  isi
    3. 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
    4. 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
    5. 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
    6. 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
    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. 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
    9. 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
    10. 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
    11. 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
    12. 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
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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