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The Complete Solution of the Long‐Wave–Short‐Wave Resonance Equations
Author(s) -
Ma YanChow
Publication year - 1978
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1978593201
Subject(s) - inverse scattering transform , soliton , resonance (particle physics) , physics , inverse scattering problem , inhomogeneous electromagnetic wave equation , wave equation , integral equation , scattering , classical mechanics , mathematical analysis , mathematics , nonlinear system , quantum mechanics , magnetic field , optical field
We give a complete analysis of the long‐wave–short‐wave resonance equations which appear in fluid mechanics as well as plasma physics. Using the inverse‐scattering technique, these equations can be reduced to a pair of linear integral equations (Marchenko equations), with the N ‐soliton solutions intimately related to the asymptotic state of the evolution equations. The interaction of solitons and the conserved quantities are discussed.