2025/02/11 by Márcio Cavalcante, Cavalcante, Márcio, Marques, José
Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Quantum optics and atomic interactions
paper · pdf · doi:10.48550/arxiv.2502.07967
openalex publication_date 2025/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
In this paper, we establish local well-posedness for the Cauchy problem associated with the Korteweg-de Vries (KdV) equation on a general metric star graph. The graph comprises m + k semi-infinite edges: k negative half-lines and m positive half-lines, all joined at a common vertex. The choice of boundary conditions is compatible with the conditions determined by the semigroup theory. The crucial point in this work is to obtain the integral formula using the forcing operator method and the Fourier restriction method of Bourgain. This work extends the results obtained by Cavalcante for the specific case of the Y junction to a more general class of star graphs.