Fokas, A. S.; Ablowitz, M. J. The inverse scattering transform for the Benjamin-Ono equation A pivot to multidimensional problems. (English) Zbl 0505.76031 Stud. Appl. Math. 68, 1-10 (1983). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 93 Documents MSC: 76B25 Solitary waves for incompressible inviscid fluids 76B47 Vortex flows for incompressible inviscid fluids 35R30 Inverse problems for PDEs 35Q99 Partial differential equations of mathematical physics and other areas of application Keywords:Benjamin-Ono equation; long internal gravity waves in stratified fluid; shear flow; inverse scattering transforms; initial value problem; linearised; closed form solution; definitive spectral characterization; Hilbert transform PDFBibTeX XMLCite \textit{A. S. Fokas} and \textit{M. J. Ablowitz}, Stud. Appl. Math. 68, 1--10 (1983; Zbl 0505.76031) Full Text: DOI References: [1] Benjamin, J. Fluid Mech. 29 pp 559– (1967) · Zbl 0147.46502 [2] Maslowe, J. Fluid Mech 101 pp 321– (1980) · Zbl 0458.76038 [3] Case, Proc. Nat. Acad. Sci. U.S.A. 75 pp 3563– (1978) · Zbl 0449.35085 [4] Chen, Phys. Fluids 22 pp 187– (1979) [5] Nakamura, J. Phys. Soc. Japan 47 pp 1701– (1979) · Zbl 1334.35006 [6] Boch, Phys. Lett. 74 pp l73– (1979) [7] Fokas, Phys. Lett. 86 pp 341– (1981) [10] Muskhelishvili, Singular Integral Equations (1953) [11] Gakhov, Boundary Value Problems 85 (1966) [12] Kodama, Phys. Rev. Lett. 46 pp 687– (1981) [13] Ablowitz, A direct linearization associated with the Benjamin-Ono equation, Workshop of Mathematical Methods in Hydrodynamics and Integrability in Related Dynamical Systems, La Jolla, Calif. pp 7– (1981) 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.