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Continuous Families of Embedded Solitons in the Third‐Order Nonlinear Schrödinger Equation
Author(s) -
Yang J.,
Akylas T. R.
Publication year - 2003
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 - 10.1111/1467-9590.t01-1-00238
Subject(s) - soliton , transformation (genetics) , nonlinear system , nonlinear schrödinger equation , parameterized complexity , gauge (firearms) , physics , third order , order (exchange) , mathematical analysis , mathematical physics , term (time) , mathematics , classical mechanics , quantum mechanics , history , biochemistry , chemistry , philosophy , theology , archaeology , finance , combinatorics , economics , gene
The nonlinear Schrödinger equation with a third‐order dispersive term is considered. Infinite families of embedded solitons, parameterized by the propagation velocity, are found through a gauge transformation. By applying this transformation, an embedded soliton can acquire any velocity above a certain threshold value. It is also shown that these families of embedded solitons are linearly stable, but nonlinearly semi‐stable.