Arkad’ev, V. A.; Pogrebkov, A. K.; Polivanov, M. K. Singular solutions of the KdV equation and the inverse scattering method. (Russian. English summary) Zbl 0571.35094 Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 133, 17-37 (1984). 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 Cited in 1 ReviewCited in 9 Documents 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) Keywords:solvability; KdV-equation; singular initial data; inverse scattering transform; interacting particles PDFBibTeX XMLCite \textit{V. A. Arkad'ev} et al., Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 133, 17--37 (1984; Zbl 0571.35094) Full Text: EuDML