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Global dynamics with stable/unstable solitons (N. '17)
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Classroom Contents
Kenji Nakanishi - Global Dynamics Around and Away From Solitons
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- 1 Intro
- 2 Nonlinear dispersive PDEs, such as the nonlinear Klein-Gordon equation
- 3 Slightly above the ground state energy Consider the nonlinear Klein-Gordon (KG) in the energy space
- 4 Stable and unstable solitons To consider solution sets containing two distinct solitons in size, shape and stability , an easy model is the nonlinear Schrodinger equation
- 5 Mass-energy restriction
- 6 Global dynamics with stable/unstable solitons (N. '17)
- 7 2-solitons To deal with global dynamics containing multi-solitons, we consider the nonlinear Klein-Gordion with a constant o damping
- 8 Instability of the solitons
- 9 Open questions: 3-soliton and soliton merger
- 10 Open question: soliton merger
