Soliton and Rogue Wave Solution of the New Nonautonomous Nonlinear Schrodinger Equation
Soliton and Rogue Wave Solution of the New Nonautonomous Nonlinear Schrodinger Equation
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DOI：
10.1088/0253-6102/56/6/04
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发表时间：
2011-12
影响因子：
3.1
通讯作者：
Wang You-Ying;He Jing-song;Li Yishen
中科院分区：
文献类型：
--
作者：
Wang You-Ying;He Jing-song;Li Yishen
本文给出了将变系数非线性薛定谔（VCNLS）方程映射到一般非线性薛定谔（NLS）方程的一种新的（或第二类）变换。作为一种特殊情况，引入了一类具有t相关势的非自治NLS方程。在此基础上，利用新的变换，充分利用常规NLS方程的已知孤子解和异常波解，分别讨论了新的非自治NLS方程的特殊模型的相应类型的解。此外，利用新的变换，解析地给出了一类特殊VCNLS方程的异常波的一个新的表达式，即非理性公式。上面提到的两种类型的转换之间的主要区别由三项列出。（x,t） = q(x,t) p(x,t)e i * (x,t),(1)将变系数非线性薛定谔方程映射为通常的非线性薛定谔方程。根据等式。参考(1)中的(6)-(10)，如果q（X，T）是NLS方程的解
In this paper, a new type (or the second type) of transformation which is used to map the variable coefficient nonlinear Schrodinger (VCNLS) equation to the usual nonlinear Schrodinger (NLS) equation is given. As a special case, a new kind of nonautonomous NLS equation with a t-dependent potential is introduced. Further, by using the new transformation and making full use of the known soliton and rogue wave solutions of the usual NLS equation, the corresponding kinds of solutions of a special model of the new nonautonomous NLS equation are discussed respectively. Additionally, through using the new transformation, a new expression, i.e., the non-rational formula, of the rogue wave of a special VCNLS equation is given analytically. The main differences between the two types of transformation mentioned above are listed by three items. (x,t) = q(X,T)p(x,t)e i�(x,t) , (1) mapping the variable coefficient nonlinear Schrodinger (VCNLS) equation to the usual nonlinear Schrodinger (NLS) equation has been developed. According to Eqs. (6)-(10) in Ref. (1), if q(X,T) is a solution of the NLS equation