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Generalized KP II ✦ no indication of blow-up in generalized KP II 1.4 1.2 ||u|| 1 0.8 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 t 10 8 ||u y || 2 6 4 2 0 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 t Dienstag, 29. Mai 2012
Outlook ✦ Stability of KP II solutions, instability of KP I solutions, mechanism of the instability ✦ shocks in dKP ✦ Asymptotic solution for KP oscillations, Whitham equations ✦ generalized KP, blow up behavior, self-similar solutions ✦ other numerical methods, parallelization Dienstag, 29. Mai 2012
Page 1 and 2:
Numerical Study of the KP equation
Page 3 and 4:
Kadomtsev-Petviashvili equation (KP
Page 5 and 6:
Consequences of nonlocality R • c
Page 7 and 8:
• lump soliton (KPI), algebraical
Page 9 and 10:
(Line)Solitons, 2-soliton limit Die
Page 11 and 12:
Dienstag, 29. Mai 2012 (Line)Solito
Page 13 and 14:
Hyperelliptic solutions (g=2) J. Fr
Page 15 and 16:
Dienstag, 29. Mai 2012 Hyperellipti
Page 17 and 18:
KP II: perturbed KdV soliton, diffe
Page 19 and 20:
KP I: perturbed KdV soliton u 0 (x,
Page 21 and 22: KP I: perturbed KdV soliton u 0 (x,
Page 23 and 24: KP I: perturbed KdV soliton u 0 (x,
Page 25 and 26: KP I: perturbed Zaitsev solution u
Page 31 and 32: KP I: perturbed Zaitsev solution 10
Page 33 and 34: KPI: perturbed cnoidal solution ✓
Page 35 and 36: KPI: perturbed cnoidal solution =0.
Page 37 and 38: KPII: perturbed cnoidal solution =0
Page 39 and 40: Example: u 0 = sech 2 x Dienstag, 2
Page 41 and 42: Dissipative regularization u t +6uu
Page 43 and 44: Korteweg-de Vries equation u t +6uu
Page 45 and 46: Zoom in: oscillatory zone T. Grava
Page 47 and 48: Whitham equations and asymptotic so
Page 49 and 50: KdV and asymptotic solution ✏ =0.
Page 51 and 52: Dispersionless KPI (dKP, Khokhlov-
Page 53 and 54: Gradient of the dKP solution Dienst
Page 55 and 56: Dienstag, 29. Mai 2012 KP I solutio
Page 57 and 58: KP I and II solution ϵ=0.1 4 !=1 2
Page 59 and 60: Dienstag, 29. Mai 2012 KP I solutio
Page 61 and 62: Oscillatory zone shrinks with ϵ !#
Page 63 and 64: Dependence on the `weak‘ coordina
Page 65 and 66: Dienstag, 29. Mai 2012 KP II soluti
Page 67 and 68: Generalized KP equations • • eq
Page 69 and 70: Blow up u 0 (x, y) =6@ xx exp( (x 2
Page 71: critical exponent 4/3 ✦ no blowup
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