2015
DOI: 10.1007/s11071-015-2227-6
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Envelope bright- and dark-soliton solutions for the Gerdjikov–Ivanov model

Abstract: Within the context of the Madelung fluid description, investigation has been carried out on the connection between the envelope soliton-like solutions of a wide family of nonlinear Schrödinger equations and the soliton-like solutions of a wide family of Korteweg-de Vries or Korteweg-de Vries-type equations. Under suitable hypothesis for the current velocity, the Gerdjikov-Ivanov envelope solitons are derived and discussed in this paper. For a motion with the stationary profile current velocity, the fluid densi… Show more

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Cited by 123 publications
(23 citation statements)
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“…In soliton theories [1][2][3][4][5][6][7][8], as a special kind of rational solution, rogue wave has been published in different fields since Solli et al first reported the existence of optical rogue wave in 2007 [9]. Its lethality is very strong and can lead to devastated impact on the navigation.…”
Section: Introductionmentioning
confidence: 99%
“…In soliton theories [1][2][3][4][5][6][7][8], as a special kind of rational solution, rogue wave has been published in different fields since Solli et al first reported the existence of optical rogue wave in 2007 [9]. Its lethality is very strong and can lead to devastated impact on the navigation.…”
Section: Introductionmentioning
confidence: 99%
“…[4][5][6][7][8][9][10] for details). Under suitable hypothesis for the current velocity, the nonlinear Schrödinger-type equations can be put in correspondence with the Korteweg-de Vries equation, modified Kortewegde Vries equation or Gardner equation in such a manner that the soliton solutions of the latter are the squared modulus of the envelope soliton solutions of the former.…”
Section: Discussionmentioning
confidence: 99%
“…• Under suitable hypothesis for the current velocity, the Gerdjikov-Ivanov envelope solitons are similarly discussed [10]. For a motion with stationary-profile current velocity, the fluid density satisfies a generalized stationary Gardner equation, which possesses bright-, gray-and dark-type solitary waves due to corresponding parametric constraints, and finally associated envelope solitons are found for the Gerdjikov-Ivanov model.…”
Section: Introductionmentioning
confidence: 95%
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