Sasa-Satsuma higher-order nonlinear Schrodinger equation and its bilinearization and multisoliton solutions

Gilson, C., Hietarinta, J., Nimmo, J.J.C. and Ohta, Y. (2003) Sasa-Satsuma higher-order nonlinear Schrodinger equation and its bilinearization and multisoliton solutions. Physical Review E, 68(1), 016614. (doi: 10.1103/PhysRevE.68.016614)

Abstract

Higher-order and multicomponent generalizations of the nonlinear Schrödinger 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 multisoliton 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-Petviashvili hierarchy. In the process, we also get bilinearizations and multisoliton formulas for a two-component generalization of the Sasa-Satsuma equation (the Yajima-Oikawa-Tasgal-Potasek model), and for a (2+1)-dimensional generalization.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Gilson, Dr Claire and Nimmo, Dr Jonathan
• Authors: Gilson, C., Hietarinta, J., Nimmo, J.J.C., and Ohta, Y.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Physical Review E
• ISSN: 1539-3755
• ISSN (Online): 1550-2376