Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2003-04-14
Nonlinear Sciences
Exactly Solvable and Integrable Systems
13 pages in RevTex, added references
Scientific paper
10.1103/PhysRevE.68.016614
Higher order and multicomponent generalizations of the nonlinear Schrodinger equation are important in various applications, e.g., in optics. One of these equations, the integrable Sasa-Satsuma equation, has particularly interesting soliton solutions. Unfortunately the construction of multi-soliton solutions to this equation presents difficulties due to its complicated bilinearization. We discuss briefly some previous attempts and then give the correct bilinearization based on the interpretation of the Sasa-Satsuma equation as a reduction of the three-component Kadomtsev-Petvishvili hierarchy. In the process we also get bilinearizations and multi-soliton formulae for a two component generalization of the Sasa-Satsuma equation (the Yajima-Oikawa-Tasgal-Potasek model), and for a (2+1)-dimensional generalization.
Gilson C.
Hietarinta Jarmo
Nimmo J.
Ohta Yasuhiro
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