Propagation of regularity and decay of solutions to the k-generalized Korteweg-de Vries equation

2014/07/18 by Pedro Isaza, Isaza, Pedro, Felipe Linares +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1407.5110

openalex publication_date 2014/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study special regularity and decay properties of solutions to the IVP associated to the k-generalized KdV equations. In particular, for datum u₀∈ H^3/4+(\mathbb R) whose restriction belongs to H^l((b,∞)) for some l∈\mathbb Z⁺ and b∈ \mathbb R we prove that the restriction of the corresponding solution u(⋅,t) belongs to H^l((β,∞)) for any β∈ \mathbb R and any t∈ (0,T). Thus, this type of regularity propagates with infinite speed to its left as time evolves.

Citations

• On persistence properties in fractional weighted spaces

Cited by

• On the Propagation of Regularity of Solutions to the KdV Equation on the positive Half-line

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