Zakharov–Schulman system

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 ∂ t u + L 1 u = ϕ u {\displaystyle i\partial _{t}^{}u+L_{1}u=\phi u}
L 2 ϕ = L 3 ( | u | 2 ) {\displaystyle L_{2}\phi =L_{3}(|u|^{2})}

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.