Zakharov–Schulman system
Encyclopedia
In mathematics, the Zakharov–Schulman system is a system of nonlinear partial differential equation
s introduced in to describe the interactions of small amplitude, high frequency waves with acoustic wave
s.
The equations are
where L1, L2, and L3, are constant coefficient differential operator
s.
Partial differential equation
In mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...
s introduced in to describe the interactions of small amplitude, high frequency waves with acoustic wave
Acoustic wave
Acoustic waves are a type of longitudinal waves that propagate by means of adiabatic compression and decompression. Longitudinal waves are waves that have the same direction of vibration as their direction of travel. Important quantities for describing acoustic waves are sound pressure, particle...
s.
The equations are
where L1, L2, and L3, are constant coefficient differential operator
Differential operator
In mathematics, a differential operator is an operator defined as a function of the differentiation operator. It is helpful, as a matter of notation first, to consider differentiation as an abstract operation, accepting a function and returning another .This article considers only linear operators,...
s.