Rybin, A. V.; Sall’, M. A. Solitons of the Korteweg-de Vries equation on the background of a known solution. (English. Russian original) Zbl 0591.35073 Theor. Math. Phys. 63, 545-550 (1985); translation from Teor. Mat. Fiz. 63, No. 3, 333-339 (1985). Summary: Asymptotic expressions describing the propagation of solitons on the background of an arbitrary solution are obtained. A study is made of the problem of finding the phase shifts of such solitons when they interact in pairs and also when a soliton interacts with a solution that decreases with respect to x. Cited in 1 Document MSC: 35Q99 Partial differential equations of mathematical physics and other areas of application 35A22 Transform methods (e.g., integral transforms) applied to PDEs 35C20 Asymptotic expansions of solutions to PDEs Keywords:propagation of solitons; phase shifts × Cite Format Result Cite Review PDF Full Text: DOI References: [1] V. B. Matveev, Lett. Math. Phys.,3, 213 (1979). · Zbl 0418.35005 · doi:10.1007/BF00405295 [2] V. B. Matveev, Lett. Math. Phys.,3, 217 (1979). · Zbl 0421.35001 · doi:10.1007/BF00405296 [3] A. I. Bobenko, V. B. Matveev, and M. A. Sall’, Dokl. Akad. Nauk SSSR,265, 1357 (1982). [4] V. B. Matveev and M. A. Sall’, Zap. Nauchn. Semin. LOMI,120, 96 (1982). [5] M. A. Sall’, Teor. Mat. Fiz.,53, 227 (1982). [6] A. I. Bobenko, Vestn. Leningr. Univ., No. 4, 14 (1982). [7] H. Wahlquist, Lect. Notes in Math.,515, 103 (1974). [8] V. I. Karpman and E. M. Maslov, ?Soliton-conserving perturbations,? Preprint No. 51 (259) [in Russian], Institute of Terrestrial Magnetism, The Ionosphere, and Radio Wave Propagation, USSR Academy of Sciences, Moscow (1979). [9] E. M. Maslov, ?Perturbation theory for solitons in the second approximation,? Preprint No. 5 (234) [in Russian], Institute of Terrestrial Magnetism, The Ionosphere, and Radio Wave Propagation, USSR Academy of Sciences, Moscow (1979). [10] P. L. E. Uslenghi (ed.), Nonlinear Electromagnetics, New York (1980). [11] M. Wadati, J. Phys. Soc. Jpn.,52, No. 8 (1983). [12] R. M. Miura, C. S. Gardner, and M. D. Kruskal, J. Math. Phys.,9, 1204 (1968). · Zbl 0283.35019 · doi:10.1063/1.1664701 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.