Squared Eigenfunctions for the Sasa-Satsuma Equation
Squared Eigenfunctions for the Sasa-Satsuma Equation
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DOI：
10.1063/1.3075567
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发表时间：
2009-02
影响因子：
1.3
通讯作者：
Jianke Yang;D. Kaup
中科院分区：
文献类型：
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作者：
Jianke Yang;D. Kaup
平方本征函数是满足可积方程的线性化方程的Jost函数和伴随Jost函数的二次组合。它们是可积方程相关的各种研究所需要的，如孤子微扰理论的发展。本文导出了Sasa-Satsuma方程的平方本征函数，该方程的谱算子为3×3系统，而线性化算子为2×2系统。它示出，这些平方特征函数是两项的总和，其中每一项是一个产品的Jost功能和伴随Jost功能。推导过程分两步：第一步是利用Riemann-Hilbert方法，通过散射数据的变化来计算势的变化。第二种方法是通过初等计算由势的变化计算散射数据的变化。虽然这个过程已被用于其他可积方程之前，它是在这里，为.
Squared eigenfunctions are quadratic combinations of Jost functions and adjoint Jost functions which satisfy the linearized equation of an integrable equation. They are needed for various studies related to integrable equations, such as the development of its soliton perturbation theory. In this article, squared eigenfunctions are derived for the Sasa–Satsuma equation whose spectral operator is a 3×3 system, while its linearized operator is a 2×2 system. It is shown that these squared eigenfunctions are sums of two terms, where each term is a product of a Jost function and an adjoint Jost function. The procedure of this derivation consists of two steps: First is to calculate the variations of the potentials via variations of the scattering data by the Riemann–Hilbert method. The second one is to calculate the variations of the scattering data via the variations of the potentials through elementary calculations. While this procedure has been used before on other integrable equations, it is shown here, for ...