论文标题
新的可集成的多莱维索引和混合分数非线性孤子层层次结构
New Integrable Multi-Lévy-Index and Mixed Fractional Nonlinear Soliton Hierarchies
论文作者
论文摘要
在这封信中，我们提出了一个简单而新的想法，可以生成两种新型的可集成多莱维索引和混合 - 莱维 - 索引（混合）分数非线性孤子层，其中包含多索引和混合分数高级非级非线性非线性schrödinger（nls）层次层次（NLS），分数复杂的kortifient kortifient Kortifiend Kortifiend Kortefifient Kortified Kortef and Frified Kortef and Frractrach（C. C. C. C. C. C. c. c. c. c. c。 MKDV层次结构。可以使用平方本征函数的完整性给出它们的明确表格。此外，我们通过线性化提出了它们的异常分散关系，并通过矩阵Riemann-Hilbert问题通过反向散射变换来介绍分数多丝溶液。这些获得的分数多螺旋溶液可能有助于了解多索引分数非线性培养基中非线性波的相关超分散转运。
In this letter, we present a simple and new idea to generate two types of novel integrable multi-Lévy-index and mix-Lévy-index (mixed) fractional nonlinear soliton hierarchies, containing multi-index and mixed fractional higher-order nonlinear Schrödinger (NLS) hierarchy, fractional complex modified Korteweg-de Vries (cmKdV) hierarchy, and fractional mKdV hierarchy. Their explicit forms can be given using the completeness of squared eigenfunctions. Moreover, we present their anomalous dispersion relations via their linearizations, and fractional multi-soliton solutions via the inverse scattering transform with matrix Riemann-Hilbert problems. These obtained fractional multi-soliton solutions may be useful to understand the related super-dispersion transports of nonlinear waves in multi-index fractional nonlinear media.
