Green's function for the fractional KdV equation on the periodic domain via Mittag-Leffler function

DOI10.1515/fca-2021-0063zbMath1498.35582arXiv2101.02269OpenAlexW4206810995MaRDI QIDQ2059225

Uyen Le, Dmitry E. Pelinovsky

Publication date: 13 December 2021

Published in: Fractional Calculus \& Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2101.02269

zbMATH Keywords

Mittag-Leffler functionGreen's functionfractional Laplacianperiodic domainpositivity and monotonicity

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Mittag-Leffler functions and generalizations (33E12) Fractional partial differential equations (35R11)

Related Items (1)

On the Green function of the killed fractional Laplacian on the periodic domain

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Uniqueness of non-linear ground states for fractional Laplacians in \(\mathbb{R}\)
• Periodic traveling-wave solutions of nonlinear dispersive evolution equations
• Maximum principles for fractional differential equations derived from Mittag-Leffler functions
• Interactions of solitons in nonintegrable systems: direct perturbation method and applications
• Functional analysis, Sobolev spaces and partial differential equations
• Nondegeneracy and stability of antiperiodic bound states for fractional nonlinear Schrödinger equations
• Further study on periodic solutions of elliptic equations with a fractional Laplacian
• Correction to: ``Periodic waves in the fractional modified Korteweg-de Vries equation
• What is the fractional Laplacian? A comparative review with new results
• Two-pulse solutions in the fifth-order KdV equation: rigorous theory and numerical approximations
• Kink dynamics in a nonlinear beam model
• Fractional Laplacian on the torus
• Stability of Small Periodic Waves in Fractional KdV-Type Equations
• Stability of Periodic Traveling Waves for Nonlinear Dispersive Equations
• On the existence of periodic solutions for a fractional Schrödinger equation
• Existence of periodic travelling-wave solutions of nonlinear, dispersive wave equations
• Mittag-Leffler Functions, Related Topics and Applications
• Stability of periodic waves for the fractional KdV and NLS equations
• Convergence of Petviashvili's Method near Periodic Waves in the Fractional Korteweg--de Vries Equation
• The completely monotonic character of the Mittag-Leffler function 𝐸ₐ(-𝑥)
• Positive solutions for boundary value problem of nonlinear fractional differential equation

This page was built for publication: Green's function for the fractional KdV equation on the periodic domain via Mittag-Leffler function