Positive periodic solutions for the Korteweg-de Vries equation
Date
2007-04-04
Authors
Georgiev, Svetlin G.
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
In this paper we prove that the Korteweg-de Vries equation
∂tu + ∂3xu + u∂xu = 0
has unique positive solution u(t, x) which is ⍵-periodic with respect to the time variable t and u(0, x) ∈ Ḃγp,q ([α, b]), γ > 0, γ ∉ {1, 2,...}, p > 1, q ≥ 1, α < b are fixed constants, x ∈ [α, b]. The period ⍵ > 0 is arbitrary chosen and fixed.
Description
Keywords
Nonlinear evolution equation, Kortewg de Vries equation, Periodic solutions
Citation
Georgiev, S. G. (2007). Positive periodic solutions for the Korteweg-de Vries equation. <i>Electronic Journal of Differential Equations, 2007</i>(49), pp. 1-13.
Rights
Attribution 4.0 International