Solitons.

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Presentation transcript:

solitons

Nonlinear waves & solitons

Linear dispersion relation b

Reductive perturbation method KdV equation

KdV equation

KdV equation

Pulse solution Pulse solution KdV equation Pulse solution Pulse solution

KdV equation

KdV equation Solitary Wave

KdV equation Solitary Wave

Simplified model -- collision

Solitary waves in water

Fermi, Pasta, and Ulam recurrence phenomena sinewave sinewave

Fermi, Pasta, and Ulam recurrence phenomena b 2b b* b o nonlinear dispersion

Fermi, Pasta, and Ulam recurrence phenomena b 2b b* b o

Fermi, Pasta, and Ulam recurrence phenomena Equal amplitudes

Fermi, Pasta, and Ulam recurrence phenomena Equal amplitudes

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

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

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