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Singular solutions of the KdV equation and the inverse scattering method. (Russian. English summary) Zbl 0571.35094

The solvability of the KdV-equation with singular initial data is investigated using the inverse scattering transform method. A class of solutions rapidly decreasing at infinity with a finite number of poles is described. The pole dynamics is interpreted as interacting particles on a line.
Reviewer: P.Holod

MSC:

35Q99 Partial differential equations of mathematical physics and other areas of application
35G25 Initial value problems for nonlinear higher-order PDEs
35R30 Inverse problems for PDEs
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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