Geodesic
Integrable twofold hierarchy of perturbed equations and application to optical soliton dynamics
Teoretičeskaâ i matematičeskaâ fizika, Tome 167 (2011) no. 3, pp. 465-478

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We construct well-known integrable equations with their Lax pairs from the corresponding linear equations using our nonlinearization scheme. Using negative powers in the spectral flow to deform the time Lax operator, we find a class of perturbations that unlike the usual perturbations, which spoil the system integrability, exhibit a twofold integrable hierarchy, including those for the KdV, modified KdV, sine-Gordon, nonlinear Schrödinger (NLS), and derivative NLS equations. We discover hidden possibilities of using the perturbed hierarchy of the NLS equations to amplify and control optical solitons propagating through a fiber in a doped nonlinear resonant medium.
Mots-clés : Lax pair
Keywords: nonlinearization of linear equation, nonholonomic deformation, optical soliton, nonlinear Schrödinger soliton, self-induced transparency soliton, integrable hierarchy. 
@article{TMF_2011_167_3_a10,
     author = {A. Kundu},
     title = {Integrable twofold hierarchy of perturbed equations and application to optical soliton dynamics},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {465--478},
     publisher = {mathdoc},
     volume = {167},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2011_167_3_a10/}
}
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A. Kundu. Integrable twofold hierarchy of perturbed equations and application to optical soliton dynamics. Teoretičeskaâ i matematičeskaâ fizika, Tome 167 (2011) no. 3, pp. 465-478. http://geodesic.mathdoc.fr/item/TMF_2011_167_3_a10/