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 :

i\partial_t^ u + L_1u = \phi u

L_2 \phi = L_3( ,  u , ^2)

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 ...

References

* {{DEFAULTSORT:Zakharov-Schulman system Partial differential equations Acoustics