2018/08/02 by Tetsu Mizumachi, Mizumachi, Tetsu · 1 citation
Mathematics · Physics and Astronomy · #37K40 #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 #Primary 35B35 #Secondary 35Q35
paper · pdf · doi:10.48550/arxiv.1808.00809
openalex publication_date 2018/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The KP-II equation was derived by [B. B. Kadomtsev and V. I. Petviashvili,Sov. Phys. Dokl. vol.15 (1970), 539-541] to explain stability of line solitary waves of shallow water. Stability of line solitons has been proved by [T. Mizumachi, Mem. of vol. 238 (2015), no.1125] and [T. Mizumachi, Proc. Roy. Soc. Edinburgh Sect. A. vol.148 (2018), 149--198]. It turns out the local phase shift of modulating line solitons are not uniform in the transverse direction. In this paper, we obtain the L^∞-bound for the local phase shift of modulating line solitons for polynomially localized perturbations.