Geodesic
Periodic and Solitary Wave Solutions of Two Component Zakharov–Yajima–Oikawa System, Using Madelung's Approach
Symmetry, integrability and geometry: methods and applications, Tome 7 (2011) Cet article a éte moissonné depuis la source Math-Net.Ru

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Using the multiple scales method, the interaction between two bright and one dark solitons is studied. Provided that a long wave-short wave resonance condition is satisfied, the two-component Zakharov–Yajima–Oikawa (ZYO) completely integrable system is obtained. By using a Madelung fluid description, the one-soliton solutions of the corresponding ZYO system are determined. Furthermore, a discussion on the interaction between one bright and two dark solitons is presented. In particular, this problem is reduced to solve a one-component ZYO system in the resonance conditions.
Keywords: dark-bright solitons; nonlinear Schrödinger equation; Zakharov–Yajima–Oikawa system; Madelung fluid approach. 
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     author = {Anca Visinescu and Dan Grecu and Renato Fedele and Sergio De Nicola},
     title = {Periodic and {Solitary} {Wave} {Solutions} of {Two} {Component} {Zakharov{\textendash}Yajima{\textendash}Oikawa} {System,} {Using} {Madelung's} {Approach}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2011},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a40/}
}
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Anca Visinescu; Dan Grecu; Renato Fedele; Sergio De Nicola. Periodic and Solitary Wave Solutions of Two Component Zakharov–Yajima–Oikawa System, Using Madelung's Approach. Symmetry, integrability and geometry: methods and applications, Tome 7 (2011). http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a40/

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