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In mathematics, the Zakharov–Schulman system is a system of nonlinear partial differential equations introduced in (Zakharov & Schulman 1980) to describe the interactions of small amplitude, high frequency waves with acoustic waves. 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 operators.
References

V.E. Zakharov, E.I. Schulman, Degenerated dispersion laws, motion invariant and kinetic equations, Physica 1D (1980), 185-250.