Ablowitz, Mark J.; Kaup, David J.; Newell, Alan C.; Segur, Harvey The inverse scattering transform-Fourier analysis for nonlinear problems. (English) Zbl 0408.35068 Studies Appl. Math. 53, 249-315 (1974). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 21 ReviewsCited in 769 Documents MSC: 35P25 Scattering theory for PDEs 35G10 Initial value problems for linear higher-order PDEs 35K25 Higher-order parabolic equations 45K05 Integro-partial differential equations 35A22 Transform methods (e.g., integral transforms) applied to PDEs Keywords:Evolution Equations; Inverse Scattering; Integro-Differential Operator; Baucklund Transformations; Dispersion Relation; Fourier Transforms PDF BibTeX XML Cite \textit{M. J. Ablowitz} et al., Stud. Appl. Math. 53, 249--315 (1974; Zbl 0408.35068) Full Text: DOI References: [1] Ablowitz, Phys. Rev. Lett. 30 pp 1262– (1973a) [2] Ablowitz, Phys. Rev. Lett. 31 pp 125– (1973b) · Zbl 1243.35143 [3] J. Math. Phys. [4] Ablowitz, J. Math. Phys. 14 pp 1277– (1973) · Zbl 0261.35070 [5] Bean, Bull. Amer. Phys. Soc. 4 pp 53– (1959) [6] Benjamin, Philos. Trans. Roy. Soc. A272 pp 47– (1972) · Zbl 0229.35013 [7] Benjamin, Lectures in Applied Math. 15 (1974) [8] Benney, Lectures in Applied Math. 15 (1974) [9] Benney, J. Math. & Phys. 46 pp 133– (1967) · Zbl 0153.30301 [10] Berezin, Sov. Phys.-JETP. 19 (5) pp 1265– (1964) [11] Bespalov, Nonlinear Optics Collection of Papers (1968) [12] Clairin, Ann. Toulouse 5 (2) pp 437– (1903) · JFM 34.0388.05 [13] Cole, Quart. Appl. Math. 9 pp 225– (1951) · Zbl 0043.09902 [14] Enz, Phys. Rev. 131 pp 1392– (1963) · Zbl 0136.23604 [15] Faddeev, Dokl. Akad. Nauk. SSSR 121 pp 63– (1958) [16] Fergason, J. Amer. Oil Chemists Soc. 45 pp 120– (1968) [18] Frenkel, J. Phys.(USSR) 1 pp 137– (1939) [20] Gardner, Phys. Rev. Lett. 19 pp 1095– (1967) [21] Gasymov, Dokl. Akad, Nauk. SSSR 167 pp 495– (1966a) [22] 167 [23] Gel’fand, Amer. Math. Soc. Transl. 1 (2) pp 253– (1951) [24] Gibbon, Lett. Nuove Cimento 8 (13) pp 775– (1973) [25] Hirota, Phys. Rev. Lett. 27 pp 1192– (1971) · Zbl 1168.35423 [26] Hirota, J. Math. Phys. 14 pp 810– (1973) · Zbl 0261.76008 [27] Karpman, Phys. Lett. 25A pp 708– (1967) [28] Karpman, Phys. Lett. 26A pp 619– (1968) [29] Kelley, Phys. Rev. Lett. 15 (1965) [30] Kochendorfer, Z. Phys. 127 pp 533– (1950) [31] Korteweg, Phil. Mag. 39 pp 422– (1895) [32] Kruskal, Proc. Conf. on Math. Models in the Physical Sciences, Univ. of Notre Dame, South Bend, Ind. 17 (1962) [33] Kruskal, Lectures in Applied Math 15 (1974) [34] Lamb, Rev. Mod. Phys. 43 pp 99– (1971) [35] Lamb, Phys. Rev. Lett. 31 pp 196– (1973) [38] Landau, Quantum Mechanics (1965) [39] Lax, C.D.A.M. 21 pp 467– (1968) [40] Leibovich, F. Fluid Mech. 42 pp 903– (1970) [41] Lewis, ORSI Symp. Proc. (1966) [42] Marchenko, Dokl. Akad. Nauk. SSSR 104 pp 695– (1955) [44] McLaughlin, J. Math. Phys. 14 (12) pp 1817– · Zbl 0268.35053 [45] Miura, J. Math. Phys. 1 pp 1202– (1968) · Zbl 0283.35018 [47] Peregrine, J. Fluid Mech. 25 pp 321– (1966) [48] Russell, Proc. Roy. Soc. pp 319– (1844) [49] Segur, J. Fluid Mech. 59 pp 721– (1973) · Zbl 0265.76027 [50] Scott, Solid-State Electron 7 pp 137– (1964) [51] Scott, Proceedings of The I.E.E.E. 61 pp 1449– (1973) [52] Skyrme, Proc. Roy. Soc. A247 pp 260– (1958) [53] Skyrme, Proc. Roy. Soc. A262 pp 237– (1961) · Zbl 0099.43605 [54] Talanov, JETP Lett. 2 pp 141– (1967) [57] Washimi, Phys. Rev. Lett. 17 pp 996– (1966) [58] Wijngaarden, J. Fluid Mech. 33 pp 465– (1968) · Zbl 0187.52202 [59] Zabusky, Academic Press pp 223– (1967) [60] Zabusky, Phys. Rev. Lett. 15 pp 240– (1965) · Zbl 1201.35174 [61] Zakharov, Funct. Anal. and Appl. 5 pp 18– (1971) [62] Zakharov, Soviet Phys. JETP Lett. 18 pp 243– (1973) [63] Zakharov, Sov. Phys. JETP. 34 pp 62– (1972) 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.