New integrable multi-Lévy-index and mixed fractional nonlinear soliton hierarchies

DOI10.1016/j.chaos.2022.112758OpenAlexW4304092833MaRDI QIDQ2680113

Zhenya Yan

Publication date: 26 January 2023

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2208.13393

zbMATH Keywords

Riemann-Hilbert problemsolitonsinverse scatteringanomalous dispersion relationintegrable fractional systemmulti-Lévy-index and mix-index fractional soliton hierarchy

Mathematics Subject Classification ID

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)

Related Items (7)

Nondegenerate solitons in the integrable fractional coupled Hirota equation ⋮ Data-driven soliton mappings for integrable fractional nonlinear wave equations via deep learning with Fourier neural operator ⋮ Solitons in a coupled system of fractional nonlinear Schrödinger equations ⋮ The Riemann-Hilbert approach for the higher-order Gerdjikov-Ivanov equation, soliton interactions and position shift ⋮ Inverse scattering transform for the integrable fractional derivative nonlinear Schrödinger equation ⋮ Fractional advection diffusion asymmetry equation, derivation, solution and application ⋮ Interactions of fractional \(N\)-solitons with anomalous dispersions for the integrable combined fractional higher-order mKdV hierarchy

Cites Work

• Unnamed Item
• Unnamed Item
• Closure of the squared Zakharov-Shabat eigenstates
• A predictor-corrector approach for the numerical solution of fractional differential equations
• On Riesz derivative
• L'intégrale de Riemann-Liouville et le problème de Cauchy
• An Extension of Nonlinear Evolution Equations of the K-dV (mK-dV) Type to Higher Orders
• Functional Fractional Calculus
• Direct and inverse scattering transforms with arbitrary spectral singularities
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• Method for Solving the Korteweg-deVries Equation
• Fractional differentiation matrices with applications
• Exact envelope-soliton solutions of a nonlinear wave equation
• The random walk's guide to anomalous diffusion: A fractional dynamics approach

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