Geodesic
Some new methods and results in the theory of ($2+1$)-dimensional integrable equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 99 (1994) no. 2, pp. 185-200 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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M. Boiti; F. Pempinelli; A. K. Pogrebkov. Some new methods and results in the theory of ($2+1$)-dimensional integrable equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 99 (1994) no. 2, pp. 185-200. http://geodesic.mathdoc.fr/item/TMF_1994_99_2_a3/

[1] M. Boiti, F. Pempinelli, A. K. Pogrebkov, M. C. Polivanov, “Resolvent approach for the nonstationaiy Schrodinger equation (standard case of rapidly decreasing potential”, Proceedings of the seventh Workshop on Nonlinear Evolution Equations and Dynamical Systems (NEEDS'91), World Scientific Pub. Co., Singapore, 1992 | MR

[2] M. Boiti, F. Pempinelli, A. K. Pogrebkov, M. C. Polivanov, Theor. Math. Phys., 93 (1992), 1200–1224 | DOI | MR | Zbl

[3] M. Boiti, F. Pempinelli, A. K. Pogrebkov, M. C. Polivanov, Inverse problems, 8 (1992), 331 | DOI | MR | Zbl

[4] B. B. Kadomtsev, V. I. Petviashvili, Sov. Phys. Doklady, 192 (1970), 539 | Zbl

[5] V. Dryuma, Sov. Phys. J. Exp. Theor. Phys. Lett., 19 (1974), 381

[6] V. E. Zakharov, S. V. Manakov, Sov. Sci. Rev.–Phys. Rev., 1 (1979), 133; S. V. Manakov, Physica D, 3 (1981), 420 | DOI | MR | Zbl

[7] M. J. Ablowitz, H. Segur, J. Fluid Mech., 92 (1979), 691 | DOI | MR | Zbl

[8] A. S. Fokas, M. J. Ablowitz, Stud. Appl. Math., 69 (1983), 211 | DOI | MR | Zbl

[9] R. Beals, R. R. Coifman, Comm. Pure. Appl. Math., 37 (1984), 39 ; 38 (1985), 29 | DOI | MR | Zbl | DOI | MR | Zbl

[10] S. P. Novikov, S. V. Manakov, L. P. Pitaevskii, V. E. Zakharov, Theory ofSolitons. The method of Inverse Scattering, Plenum, New York, 1984 | MR | Zbl

[11] M. Boiti, J. Léon, F. Pempinelli, Phys. Lett. A, 141 (1989), 96 | DOI | MR

[12] V. G. Bakurov, Phys. Lett. A, 160 (1991), 367 | DOI | MR

[13] M. J. Ablowitz, J. Villarroel, Stud. Appl. Math., 85 (1991), 195 | DOI | MR | Zbl

[14] A. S. Fokas, V. E. Zakharov, J. Nonlinear Sci., 2 (1992), 109–134 | DOI | MR | Zbl

[15] M. Boiti, F. Pempinelli, A. Pogrebkov, “Solutions of the KPI equation with smooth initial data”, Inverse Problems, 10:3 (1994), 505–519 | DOI | MR | Zbl

[16] M. Boiti, F. Pempinelli, A. Pogrebkov, “Properties of solutions of the Kadomtsev-Petviashvili I equation”, J. Math. Phys., 35:9 (1994), 4683–4718 | DOI | MR | Zbl

[17] M. Boiti, F. Pempinelli, A. K. Pogrebkov, M. C. Polivanov, Inverse problems, 7 (1991), 43–56 | DOI | MR | Zbl

[18] S. V. Manakov, private communication

[19] M. J. Ablowitz, S. V. Manakov, C. L. Shultz, Phys. Lett. A, 148 (1990), 50 | DOI | MR