Patterns and waves
NLS
1D, σ ≠ 0
1D, σ = 0
2D, σ = 1
2D, 3D, σ = 0
KG
1D kinks
Compact structures
Q-balls
1D
2D
3D
Q-vortices
Stationary
Moving
Formation and Evolution of Compact Patterns
Evolution of vortices in time (real part - r and absolute value - a).
Ia
Fig. 8, bottom -- δ=2/3, m=2, a=b=1, σ=0, ω=2, n=3
IIr
δ=1/3, m=2, a=b=1, σ=0, ω=1.6, n=1
IIIr
δ=1/3, m=2, a=b=1, σ=1, ω=1.74, n=1