1990
DOI: 10.1088/0305-4470/23/12/017
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A direct approach to studying soliton perturbations

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Cited by 85 publications
(68 citation statements)
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“…The solution thus constructed has been used extensively to develop a direct perturbation theory for the KdV equation [22,23] The above results coincide with those derived by IST [14].…”
Section: Detailed Description Of the Phase Shiftsupporting
confidence: 69%
See 1 more Smart Citation
“…The solution thus constructed has been used extensively to develop a direct perturbation theory for the KdV equation [22,23] The above results coincide with those derived by IST [14].…”
Section: Detailed Description Of the Phase Shiftsupporting
confidence: 69%
“…Recently, a similar direct approach has been introduced by Herman [22], Kalyakin [23], and Konotop and Vekslerchik [24] to study the higher-order effects. [32].…”
Section: Introductionmentioning
confidence: 99%
“…For linearization around singlesoliton solutions, these complete eigenfunctions have been obtained for a large class of integrable equations, such as the KdV hierarchy, NLS hierarchy, modified-KdV hierarchy, sine-Gordon, and Benjamin-Ono equations [2][3][4][5][6][7][8][9]. It has been found that these eigenfunctions are related to squared eigenfunctions of the associated eigenvalue problem (except for the Benjamin-Ono equation).…”
Section: Introductionmentioning
confidence: 99%
“…One idea by Keener and McLaughlin [2] is that eigenfunctions of a linearization operator expanded around an arbitrary solution are the variations of the solution with respect to each parameter in the scattering data. Another idea by Herman [6] is to utilize the Lax pair of the integrable equation and find special combinations of squared eigenfunctions of the associated eigenvalue problem, so that these combinations satisfy the linearized equation of the evolution equation. However, in both approaches, each equation has to be treated separately.…”
Section: Introductionmentioning
confidence: 99%
“…so-called bright solitons, has been developed over many years (cf. Karpman & Maslov 1977;Kodama & Ablowitz 1981;Herman 1990). The analytical work employs a diverse set of methods including perturbations of the inverse scattering transform (IST), multi-scale perturbation analysis, perturbations of conserved quantities, etc.…”
mentioning
confidence: 99%