Physics:Zakharov–Schulman system

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

[math]\displaystyle{ i\partial_t^{} u + L_1u = \phi u }[/math]

[math]\displaystyle{ L_2 \phi = L_3( | u |^2) }[/math]

where L₁, L₂, and L₃, are constant coefficient differential operators.

References

• Zakharov, V.E.; Schulman, E.I. (1980). "Degenerated dispersion laws, motion invariant and kinetic equations". Physica D 1: 185–250. doi:10.1016/0167-2789(80)90011-1.