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.

External links

Zakharov-Schulman_system at the Dispersive PDE Wiki

Undergraduate Texts in Mathematics

Graduate Studies in Mathematics

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