New Integrable Multi-L\'evy-Index and Mixed Fractional Nonlinear Soliton Hierarchies
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Publication:6409093
DOI10.1016/J.CHAOS.2022.112758arXiv2208.13393MaRDI QIDQ6409093
Publication date: 29 August 2022
Abstract: In this letter, we present a simple and new idea to generate two types of novel integrable multi-L'evy-index and mix-L'evy-index (mixed) fractional nonlinear soliton hierarchies, containing multi-index and mixed fractional higher-order nonlinear Schr"odinger (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.
Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) NLS equations (nonlinear Schrödinger equations) (35Q55) Riemann-Hilbert problems in context of PDEs (35Q15) Soliton solutions (35C08) Fractional partial differential equations (35R11)
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