Geodesic
On a solution of the Cauchy problem for the Boiti–Leon–Pempinelli equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 109 (1996) no. 2, pp. 163-174 Cet article a éte moissonné depuis la source Math-Net.Ru

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Cauchy problem for the $2+1$-dimensional nonlinear Boiti–Leon–Pempinelli (BLP) equation in the framework of the Inverse Problem Method is considered. We derive evolution equations for the resolvent, Jost solutions and Spectral Data of the two-dimensional differential Klein–Gordon operator with variable coefficients that are generated by the considered BLP system of equations. Additional conditions on the Spectral Data that guarantee stability of the solutions of the Cauchy problem, are obtained. We present a recursion procedure for construction of polynomial integrals of motion and generating function of these integrals in terms of Spectral Data. 
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     author = {A. K. Pogrebkov and T. I. Garagash},
     title = {On a~solution of the {Cauchy} problem for the {Boiti{\textendash}Leon{\textendash}Pempinelli} equation},
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A. K. Pogrebkov; T. I. Garagash. On a solution of the Cauchy problem for the Boiti–Leon–Pempinelli equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 109 (1996) no. 2, pp. 163-174. http://geodesic.mathdoc.fr/item/TMF_1996_109_2_a0/

[1] T. I. Garagash, A. K. Pogrebkov, TMF, 102 (1995), 163–182 | MR | Zbl

[2] T. I. Garagash, A. K. Pogrebkov, “Resolvent method for Two–dimensional Inverse Problems”, Nonlinear evolution equations and dynamical systems, eds. V. Makhankov, I. Puzynin, O. Pashaev, World. Sci., Singapore, 1992, 124–130 | MR

[3] M. Boiti, J. Leon, F. Pempinelli, Inverse Problems, 3 (1987), 37–49 | DOI | MR | Zbl

[4] M. Boiti, F. Pempinelli, A. K. Pogrebkov, M. C. Polivanov, “Resolvent approach for the nonstationary Schrödinger 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

[5] M. Boiti, F. Pempinelli, A. K. Pogrebkov, M. K. Polivanov, TMF, 93 (1992), 181–210 | MR | Zbl

[6] M. Boiti, F. Pempinelli, A. K. Pogrebkov, TMF, 99 (1994), 185–200 | MR | Zbl

[7] M. Boiti, F. Pempinelli, A. Pogrebkov, Inverse Problems, 10 (1994), 505–519 | DOI | MR | Zbl