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 
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/
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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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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[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

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[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