Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2011-02-09
SIGMA 7 (2011), 041, 11 pages
Nonlinear Sciences
Exactly Solvable and Integrable Systems
based on a talk at Symmetries and Integrability of Difference Equations (SIDE-9), Varna, Bulgaria, June 2010
Scientific paper
10.3842/SIGMA.2011.041
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.
de Nicola Sergio
Fedele Renato
Grecu Dan
Visinescu Anca
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