Sasa-Satsuma higher-order nonlinear Schrodinger equation and its bilinearization and multisoliton solutions
Sasa-Satsuma higher-order nonlinear Schrodinger equation and its bilinearization and multisoliton solutions
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DOI：
10.1103/physreve.68.016614
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发表时间：
2003-07-01
影响因子：
2.4
通讯作者：
Ohta, Y
中科院分区：
文献类型：
--
作者：
Gilson, C;Hietarinta, J;Ohta, Y
非线性薛定谔方程的高阶和多分量推广在各种应用中是重要的，例如，在光学上。其中一个方程，可积的Sasa-Satsuma方程，具有特别有趣的孤子解。不幸的是，该方程的多孤子解的建设提出了困难，由于其复杂的双线性化。我们简要地讨论了以前的一些尝试，然后给出正确的双线性化的基础上的解释的Sasa萨摩方程作为一个减少的三个组件Kadomtsev Petviashvili层次。在此过程中，我们还得到了Sasa-Satsuma方程的两分量推广（Yajima-Oikawa-Tasgal-Potasek模型）和（2+1）维推广的双线性化和多孤子公式。
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 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.