Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 7 (2011), 041, 11 pages      arXiv:1102.1801      https://doi.org/10.3842/SIGMA.2011.041
Contribution to the Proceedings of the Conference “Symmetries and Integrability of Difference Equations (SIDE-9)”

Periodic and Solitary Wave Solutions of Two Component Zakharov-Yajima-Oikawa System, Using Madelung's Approach

Anca Visinescu a, Dan Grecu a, Renato Fedele b and Sergio De Nicola c
a) Department of Theoretical Physics, National Institute for Physics and Nuclear Engineering, Bucharest, Romania
b) Dipartimento di Scienze Fisiche, Universita Federico II and INFN Sezione di Napoli, Napoli, Italy
c) Istituto Nazionale di Ottica del Consiglio Nazionale delle Ricerche, Pozuolli, (Na), Italy

Received February 10, 2011, in final form April 19, 2011; Published online April 23, 2011

Abstract
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.

Key words: dark-bright solitons; nonlinear Schrödinger equation; Zakharov-Yajima-Oikawa system; Madelung fluid approach.

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