Geodesic
Solution of the Korteweg-de Vriez equation by the method of inverse scattering problem
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2006), pp. 16-20.

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Cauchy's problem for the nonlinear Korteweg-de Vriez equation is considered with the initial condition given by function, having certain behaviour at infinity. Construction of the solution of this problem by the method of the inverse scattering problem is described provided that the solution exists and has the same behaviour at infinity, as the initial data. 
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H. A. Asatryan; I. G. Khachatryan. Solution of the Korteweg-de Vriez equation by the method of inverse scattering problem. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2006), pp. 16-20. http://geodesic.mathdoc.fr/item/UZERU_2006_3_a0/

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[4] B.A. Marchenko, Operatory Shturma-Liuvillya i ikh prilozheniya, Naukova dumka, Kiev | MR