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

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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. Boiti^a, F. Pempinelli^a, A. K. Pogrebkov^b

^a Lecce University
^b Steklov Mathematical Institute, Russian Academy of Sciences

Full-text PDF (1565 kB) Citations (17)

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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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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:

Ion Bica, Randy Wanye K, “Modeling rogue waves with the Kadomtsev–Petviashvili (KP) equation”, Rocky Mountain J. Math., 48:5 (2018)
Boiti, M, “Scattering transform for nonstationary Schrodinger equation with bidimensionally perturbed N-soliton potential”, Journal of Mathematical Physics, 47:12 (2006), 123510
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
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
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
Boiti, M, “Extended resolvent and inverse scattering with an application to KPI”, Journal of Mathematical Physics, 44:8 (2003), 3309
Boiti, M, “Towards an inverse scattering theory for non-decaying potentials of the heat equation”, Inverse Problems, 17:4 (2001), 937
Prinari, B, “On some nondecaying potentials and related Jost solutions for the heat conduction equation”, Inverse Problems, 16:3 (2000), 589
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
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
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
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
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
A. K. Pogrebkov, M. C. Prati, “Resolvent approach to the ablowitz-ladik linear system”, Nuovo Cim B, 111:12 (1996), 1495
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
M. Boiti, F. Pempinelli, A. Pogrebkov, “Dressing of a two-dimensional nontrivial potential”, Physica D: Nonlinear Phenomena, 87:1-4 (1995), 123
Theoret. and Math. Phys., 99:2 (1994), 583–587

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

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