2006/01/11 by Thomas Kappeler, T. Kappeler, P. Perry +9
Mathematics · Physics and Astronomy · #35G25 #35Q53 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #math-ph #math.AP #math.MP #msc:35G25 #msc:35Q53
paper · pdf · doi:10.48550/arxiv.math/0601237
35 pages, new results about spectra and eigenfunctions of Schrödinger operators added, new references added
openalex publication_date 2006/01/11 · arxiv created 2007/10/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 1974 P. Lax introduced an algebro-analytic mechanism similar to the Lax L-A pair. Using it we prove global existence and uniqueness for solutions of the initial value problem for mKdV in classes of smooth functions which can be unbounded at infinity, and may even include functions which tend to infinity with respect to the space variable. Moreover, we establish the invariance of the spectrum and the unitary type of the Schrödinger operator under the KdV flow and the invariance of the spectrum and the unitary type of the impedance operator under the mKdV flow for potentials in these classes.