Darboux transformation and solitons for an integrable nonautonomous nonlinear integro-differential Schrödinger equation
Darboux transformation and solitons for an integrable nonautonomous nonlinear integro-differential Schrödinger equation
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DOI：
10.1142/s0217984917502761
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发表时间：
2017-10
影响因子：
1.9
通讯作者：
X. Yong;Yan Fan;Yehui Huang;W. Ma;Jing Tian
中科院分区：
文献类型：
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作者：
X. Yong;Yan Fan;Yehui Huang;W. Ma;Jing Tian
通过对等谱问题的格式进行修改，引入时变谱，构造了非等谱的Ablowitz-Kaup-Newell-Segur（AKNS）方程族.本文考虑了在“Multi-soliton management by the integrable nonautonomous nonlinear integro-differential Schrodinger equation”[Y. J. Zhang，D. Zhao和H. G. Luo，Ann.Phys.350（2014）112]。我们首先分析了可积性条件，并确定了模型。其次，我们修改现有的达布变换（DT）这样的非等谱问题。第三，通过得到的DT得到非自治孤子解，并讨论了这些解在非均匀介质中的基本性质，以图示说明变系数的影响。在此过程中，通过选择合适的光谱参数来代替可变的非均匀性，实现了不同类型的单孤子管理。构造了几种新型的光孤子，并给出了它们的特性。此外，还得到了四种特殊的局域双孤子解。本文讨论了在空间和时间上都具有局域性的孤子激发，这种孤子激发具有所谓的流氓波的特征，但背景为零。
By modifying the scheme for an isospectral problem, the non-isospectral Ablowitz–Kaup–Newell–Segur (AKNS) hierarchy is constructed via allowing the time varying spectrum. In this paper, we consider an integrable nonautonomous nonlinear integro-differential Schrodinger equation discussed before in “Multi-soliton management by the integrable nonautonomous nonlinear integro-differential Schrodinger equation” [Y. J. Zhang, D. Zhao and H. G. Luo, Ann. Phys. 350 (2014) 112]. We first analyze the integrability conditions and identify the model. Second, we modify the existing Darboux transformation (DT) for such a non-isospectral problem. Third, the nonautonomous soliton solutions are obtained via the resulting DT and basic properties of these solutions in the inhomogeneous media are discussed graphically to illustrate the influences of the variable coefficients. In the process, a technique by selecting appropriate spectral parameters instead of the variable inhomogeneities is employed to realize a different type of one-soliton management. Several novel optical solitons are constructed and their features are shown by some specific figures. In addition, four kinds of the special localized two-soliton solutions are obtained. The solitonic excitations localized both in space and time, which exhibit the feature of the so-called rogue waves but with a zero background, are discussed.