Solitons Waves in Mathematical Physics
The characteristics of solitary waves in integrable and near-integrable systems are indeed important topics in mathematical physics. Solitary waves generally refer to wave solutions that maintain their shape in nonlinear systems. Research on these systems involves not only mathematical theory but also practical applications in physical phenomena, such as fiber optic communications and quantum field theory.
This semester will continue from last semester’s content, focusing on the characteristics of solitary waves in integrable and near-integrable systems. The main focus will be on the unified properties of equation families, the structure of solutions, and how solitary wave solutions vary with parameters.
Additionally, in near-integrable systems with periodic potentials, the characteristics of solitary waves become more complex. Key points of focus include the stability of solitary waves, the impact of periodic potentials on solitary wave solutions, and how periodic potentials alter the propagation characteristics of solitary waves.
This semester will continue from last semester’s content, focusing on the characteristics of solitary waves in integrable and near-integrable systems. The main focus will be on the unified properties of equation families, the structure of solutions, and how solitary wave solutions vary with parameters.
Additionally, in near-integrable systems with periodic potentials, the characteristics of solitary waves become more complex. Key points of focus include the stability of solitary waves, the impact of periodic potentials on solitary wave solutions, and how periodic potentials alter the propagation characteristics of solitary waves.
Lecturer
Date
11th September ~ 4th December, 2024
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Wednesday | 13:30 - 16:55 | A3-4-312 | ZOOM 07 | 559 700 6085 | BIMSA |
Reference
1: G. Fibich. The nonlinear Schrödinger equation. Berlin: Springer, 2015.
2: M. J. Ablowitz and P. A. Clarkson. Solitons, Nonlinear evolution equations and inverse scattering. Cambridge University Press, 2001.
3: T. Miwa, M. Jimbo, E. Date. Solitons: Differential equations, symmetries and infinite dimensional algebras. Cambridge university press, 2000.
4: B. A. Malomed. Soliton management in periodic systems. Springer Science & Business Media, 2006.
5: O. Babelon, D. Bernard, M. Talon. Introduction to classical integrable systems. Cambridge University Press, 2003.
2: M. J. Ablowitz and P. A. Clarkson. Solitons, Nonlinear evolution equations and inverse scattering. Cambridge University Press, 2001.
3: T. Miwa, M. Jimbo, E. Date. Solitons: Differential equations, symmetries and infinite dimensional algebras. Cambridge university press, 2000.
4: B. A. Malomed. Soliton management in periodic systems. Springer Science & Business Media, 2006.
5: O. Babelon, D. Bernard, M. Talon. Introduction to classical integrable systems. Cambridge University Press, 2003.
Audience
Undergraduate
, Advanced Undergraduate
, Graduate
, Postdoc
Video Public
No
Notes Public
No
Language
Chinese