- 著者
- Hideshi Yamane
- 出版者
- Division of Functional Equations, The Mathematical Society of Japan
- 雑誌
- Funkcialaj Ekvacioj (ISSN:05328721)
- 巻号頁・発行日
- vol.66, no.3, pp.159-193, 2023-12-15 (Released:2023-12-13)
- 参考文献数
- 19
We solve the analytic Cauchy problem for the generalized two-component Camassa-Holm system introduced by R. M. Chen and Y. Liu. We show the existence of a unique local/global-in-time analytic solution under certain conditions. This is the first result about global analyticity for a Camassa-Holm-like system. The method of proof is basically that developed by Barostichi, Himonas and Petronilho. The main differences between their proof and ours are twofold: (i) the system of Chen and Liu is not symmetric in the two unknowns and our estimates are not trivial generalization of those in their articles, (ii) we have simplified their argument by using fewer function spaces and the main result is stated in a simple and natural way.
1 0 0 0 OA Long-time Asymptotics for the Integrable Discrete Nonlinear Schrödinger Equation: the Focusing Case
- 著者
- Hideshi Yamane
- 出版者
- Division of Functional Equations, The Mathematical Society of Japan
- 雑誌
- Funkcialaj Ekvacioj (ISSN:05328721)
- 巻号頁・発行日
- vol.62, no.2, pp.227-253, 2019 (Released:2019-08-26)
- 参考文献数
- 20
- 被引用文献数
- 1 3
We investigate the long-time asymptotics for the focusing integrable discrete nonlinear Schrödinger equation. Under generic assumptions on the initial value, the solution is asymptotically a sum of 1-solitons. We find different phase shift formulas in different regions. Along rays away from solitons, the behavior of the solution is decaying oscillation. This is one way of stating the soliton resolution conjecture. The proof is based on the nonlinear steepest descent method.