2003/07/14 by Anne Boutet de Monvel, Dmitry Shepelsky, de Monvel, Anne Boutet +1
Mathematics · Physics and Astronomy · #35Q15 #35Q53 #37K15 #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Numerical methods for differential equations #Spectral Theory (math.SP) #math.AP #math.SP #msc:35Q15 #msc:35Q53 #msc:37K15
paper · pdf · doi:10.48550/arxiv.math/0307194
LaTeX, 7 pages
arxiv created 2003/07/14 · openalex publication_date 2003/07/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We analyse an initial-boundary value problem for the mKdV equation on a finite interval by expressing the solution in terms of the solution of an associated matrix Riemann-Hilbert problem in the complex k-plane. This Riemann-Hilbert problem has explicit (x,t)-dependence and it involves certain functions of k referred to as ``spectral functions''. Some of these functions are defined in terms of the initial condition q(x,0)=q0(x), while the remaining spectral functions are defined in terms of two sets of boundary values. We show that the spectral functions satisfy an algebraic ``global relation'' that characterize the boundary values in spectral terms.