In mathematics, the Zakharov–Schulman system is a system of nonlinear
partial differential equation
In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function.
The function is often thought of as an "unknown" to be sol ...
s introduced in to describe the interactions of small amplitude, high frequency waves with
acoustic wave
Acoustic waves are a type of energy propagation through a medium by means of adiabatic loading and unloading. Important quantities for describing acoustic waves are acoustic pressure, particle velocity, particle displacement and acoustic intensit ...
s.
The equations are
:
:
where ''L''
1, ''L''
2, and ''L''
3, are constant coefficient
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 that accepts a function and return ...
s.
References
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{{DEFAULTSORT:Zakharov-Schulman system
Partial differential equations
Acoustics