Gardner, Clifford S.; Greene, John M.; Kruskal, Martin D.; Miura, Robert M. Method for solving the Korteweg-de Vries equation. (English) Zbl 1061.35520 Phys. Rev. Lett. 19, 1095-1097 (1967). Summary: A method for solving the initial-value problem of the Korteweg-de Vries equation is presented which is applicable to initial data that approach a constant sufficiently rapidly as \(| x|\to\infty\). The method can be used to predict exactly the “solitons”, or solitary waves, which emerge from arbitrary initial conditions. Solutions that describe any finite number of solitons in interaction con expressed in closed form. Cited in 2 ReviewsCited in 457 Documents MSC: 35Q53 KdV equations (Korteweg-de Vries equations) 35Q51 Soliton equations 37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems PDF BibTeX XML Cite \textit{C. S. Gardner} et al., Phys. Rev. Lett. 19, 1095--1097 (1967; Zbl 1061.35520) Full Text: DOI OpenURL References: [1] D. J. Korteweg, Phil. Mag. 39 pp 422– (1895) [2] H. Washimi, Phys. Rev. Letters 17 pp 966– (1966) [3] N. J. Zabusky, in: Mathematical Models in Physical Sciences (1963) [4] N. J. Zabusky, Phys. Rev. Letters 15 pp 240– (1965) · Zbl 1201.35174 [5] I. M. Gel’fand, Izv. Akad. Nauk SSSR, Ser. Mat. 15 pp 309– (1951) [6] I. M. Gel’fand, in: American Mathematical Society Translations (1955) [7] I. Kay, Nuovo Cimento 3 pp 276– (1956) [8] I. Kay, J. Appl. Phys. 27 pp 1503– (1956) · Zbl 0073.22202 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.