2009/08/18 by John B. Gonzalez, Gonzalez, John B.
Mathematics · Physics and Astronomy · #35Q53 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #math.AP #msc:35Q53
paper · pdf · doi:10.48550/arxiv.0908.2501
37 pages, preprint
arxiv created 2009/08/18 · openalex publication_date 2009/08/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove local existence and uniqueness of solutions of the focusing modified Korteweg - de Vries equation ut + u2ux + uxxx = 0 in classes of unbounded functions that admit an asymptotic expansion at infinity in decreasing powers of x. We show that an asymptotic solution differs from a genuine solution by a smooth function that is of Schwartz class with respect to x and that solves a generalized version of the focusing mKdV equation. The latter equation is solved by discretization methods.