Abstract
The statistical initial value problem for the envelope equation dw/dt minus gamma d**2w/dx**2 equals chi w- beta w**2w*; gamma , beta complex, is discussed. (The derivatives are both partial derivatives. ) It is shown that there exists an instability (stability) criterion which determines whether the system underlying the above equation achieves or does not achieve a monochromatic state.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 441-456 |
| Number of pages | 16 |
| Journal | SIAM Journal on Applied Mathematics |
| Volume | 27 |
| Issue number | 3 |
| DOIs | |
| State | Published - 1974 |
| Externally published | Yes |
ASJC Scopus subject areas
- Applied Mathematics