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)|
|Number of pages||16|
|Journal||SIAM Journal on Applied Mathematics|
|State||Published - 1974|
ASJC Scopus subject areas
- Applied Mathematics