Darboux Transformation of the Second-Type Derivative Nonlinear Schrödinger Equation
Darboux Transformation of the Second-Type Derivative Nonlinear Schrödinger Equation
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DOI：
10.1007/s11005-015-0758-x
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发表时间：
2015-04
影响因子：
1.2
通讯作者：
Yongshuai Zhang;Lijuan Guo;Jingsong He;Zixiang Zhou
中科院分区：
文献类型：
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作者：
Yongshuai Zhang;Lijuan Guo;Jingsong He;Zixiang Zhou
二阶导数非线性薛定谔方程（DNLSII）是在1979年作为可积模型引入的。最近，DNLSII方程已被实验证明是一个模型的光脉冲的演变，涉及自陡峭没有伴随的自相位调制。本文利用行列式构造了耦合DNLS Ⅱ方程的重Darboux变换（DT）Tn.与通常的孤立子方程的差分法相比，这种差分法是不寻常的，因为在迭代过程中，Tn包含了种子解的复杂积分。通过繁琐的分析，除了种子解的积分之外，这些积分都被消除在Tn中。此外，在一个约化条件下，这一T被约化为DNLS Ⅱ方程的DT。作为Tn的应用，给出了DNLSII方程的孤子解、有理孤子解、呼吸子解、流氓波解和多流氓波解的显式表达式。
The second-type derivative nonlinear Schrödinger (DNLSII) equation was introduced as an integrable model in 1979. Very recently, the DNLSII equation has been shown by an experiment to be a model of the evolution of optical pulses involving self-steepening without concomitant self-phase-modulation. In this paper, then-fold Darboux transformation (DT)Tnof the coupled DNLSII equations is constructed in terms of determinants. Comparing with the usual DT of the soliton equations, this kind of DT is unusual becauseTnincludes complicated integrals of seed solutions in the process of iteration. By a tedious analysis, these integrals are eliminated inTnexcept the integral of the seed solution. Moreover, thisTnis reduced to the DT of the DNLSII equation under a reduction condition. As applications ofTn, the explicit expressions of soliton, rational soliton, breather, rogue wave and multi-rogue wave solutions for the DNLSII equation are displayed.