Kida, Shigeo A vortex filament moving without change of form. (English) Zbl 0484.76030 J. Fluid Mech. 112, 397-409 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 50 Documents MSC: 76B47 Vortex flows for incompressible inviscid fluids 76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics 76D10 Boundary-layer theory, separation and reattachment, higher-order effects 76E30 Nonlinear effects in hydrodynamic stability 76V05 Reaction effects in flows Keywords:thin vortex filament; localized induction equation; nonlinear Schrödinger equation Citations:Zbl 0149.453 PDFBibTeX XMLCite \textit{S. Kida}, J. Fluid Mech. 112, 397--409 (1981; Zbl 0484.76030) Full Text: DOI Digital Library of Mathematical Functions: §19.35(ii) Physical ‣ §19.35 Other Applications ‣ Applications ‣ Chapter 19 Elliptic Integrals References: [1] Lighthill, J. Inst. Math. Applic. 1 pp 269– (1965) [2] DOI: 10.1063/1.523453 · Zbl 0351.35019 · doi:10.1063/1.523453 [3] DOI: 10.1063/1.1706500 · Zbl 0149.45302 · doi:10.1063/1.1706500 [4] DOI: 10.1017/S0022112072001107 · Zbl 0231.76013 · doi:10.1017/S0022112072001107 [5] Fraenkel, Proc. Roy. Soc. A 316 pp 29– (1970) [6] Zakharov, Sov. Phys. J. Exp. Theor. Phys. 37 pp 823– (1973) [7] DOI: 10.1017/S0022112065000915 · Zbl 0133.43803 · doi:10.1017/S0022112065000915 [8] Zakharov, Sov. Phys. J. Exp. Theor. Phys. 34 pp 62– (1972) [9] Bespalov, J. Exp. Theor. Phys. Lett. 3 pp 307– (1966) [10] DOI: 10.1007/BF01035568 · Zbl 0298.35016 · doi:10.1007/BF01035568 [11] Benney, J. Math. and Phys. 46 pp 133– (1967) · Zbl 0153.30301 · doi:10.1002/sapm1967461133 [12] DOI: 10.1017/S0022112072000928 · Zbl 0242.76023 · doi:10.1017/S0022112072000928 [13] DOI: 10.1063/1.1664797 · doi:10.1063/1.1664797 [14] DOI: 10.1063/1.1762240 · doi:10.1063/1.1762240 [15] DOI: 10.1063/1.1664975 · doi:10.1063/1.1664975 [16] Talanov, J. Exp. Theor. Phys. Lett. 2 pp 138– (1965) [17] DOI: 10.1016/0378-4371(76)90106-0 · doi:10.1016/0378-4371(76)90106-0 [18] DOI: 10.1016/0375-9601(77)90262-6 · doi:10.1016/0375-9601(77)90262-6 [19] DOI: 10.1103/PhysRevLett.15.1005 · doi:10.1103/PhysRevLett.15.1005 [20] Karpman, Sov. Phys. J. Exp. Theor. Phys. 28 pp 277– (1969) [21] DOI: 10.1143/JPSJ.31.591 · doi:10.1143/JPSJ.31.591 [22] DOI: 10.1143/JPSJ.33.805 · doi:10.1143/JPSJ.33.805 [23] DOI: 10.1017/S0022112072002307 · Zbl 0237.76010 · doi:10.1017/S0022112072002307 [24] DOI: 10.1143/JPSJ.31.293 · doi:10.1143/JPSJ.31.293 [25] DOI: 10.1063/1.1706768 · Zbl 0116.42701 · doi:10.1063/1.1706768 [26] Scott, Proc. I.E.E.E. 61 pp 1443– (1973) [27] Saffman, Stud. Appl. Math. 49 pp 371– (1970) · Zbl 0224.76032 · doi:10.1002/sapm1970494371 [28] DOI: 10.1017/S0022112061000822 · Zbl 0103.23003 · doi:10.1017/S0022112061000822 [29] Onsager, Nuovo Cimento Suppl. 6 pp 279– (1949) [30] Moore, Phil. Trans. Roy. Soc. A 272 pp 403– (1972) [31] Lighthill, Proc. Roy. Soc. A 299 pp 28– (1967) 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.