1. solitons

2. Nonlinear waves & solitons

3. Linear dispersion relationb

4. Reductive perturbation method
KdV equation

5. KdV equation

6. KdV equation

7. Pulse solution Pulse solution
KdV equation
Pulse solution
Pulse solution

8. KdV equation

9. KdV equation
Solitary
Wave

10. KdV equation
Solitary
Wave

11. Simplified model -- collision

12. Solitary waves in water

13. Fermi, Pasta, and Ulam recurrence phenomena
sinewave
sinewave

14. Fermi, Pasta, and Ulam recurrence phenomena
b b b* b o
nonlinear
dispersion

15. Fermi, Pasta, and Ulam recurrence phenomena
b b b* b o

16. Fermi, Pasta, and Ulam recurrence phenomena Equal amplitudes

17. Fermi, Pasta, and Ulam recurrence phenomena Equal amplitudes

18. Many Faces of Solitons Kanehisa Takasaki (Kyoto University)
Zabusky & kruskal
KdV soliton

19. Many Faces of Solitons Kanehisa Takasaki (Kyoto University)
Sine Gordon

20. Many Faces of Solitons Kanehisa Takasaki (Kyoto University)
mKdV soliton collision