Saturation effects in a travelling-wave parametric amplifier

Statistical Fluid Mechanics: The Mechanics of Turbulence

“…Craik (1971) considered, at the end of his paper, several exact solutions of some particular amplitude equations of the form (5.4) [for the simplest case of Eqs. (5.3) with constant coefficients C v exact solutions, represented in terms of elliptic functions, were found independently by Jurkus and Robson (1960), Armstrong et al (1962) and Bretherton (1964)]. Craik's solutions also include examples where amplitudes of some waves become infinite after a finite time.…”

“…[These publications and the book by Craik (1985) also contain many supplementary references relating to this topic] Since nonlinear dispersive waves may occur in quite different media and situations, the nonlinear wave-resonance theory has many applications to problems outside classical fluid mechanics; in such cases the theory has often been developed independently of studies of waves in ordinary fluids. As typical examples of publications dealing with three-wave resonances relating to waves of other origins, we may mention the papers by Jurkus and Robson (1960) on nonlinear electronics, by Khokhlov (1961) on electromagnetic wave propagation in dispersive conductors, and by Dimant (2000) on nonlinear interactions among ionospheric waves; the books and papers by Armstrong et al (1962), Bloembergen (1965Bloembergen ( , 1968 and Akhmanov and Khokhlov (1972) on nonlinear optics, by Davidson (1972), Weiland and Wilhelmsson (1977) and Turner and Boyd (1978) on plasma waves; and the general survey by Kaup et al (1979) [containing an extensive bibliography and supplemented by Kaup's paper (1981)]. However, in the framework of the present purposes only waves in an incompressible Navier-Stokes fluid are of interest, and in this chapter only the case of waves in nearly plane-parallel Blasius boundary-layer-flows will be investigated.…”

Quantum Instability

“…In the classical theory, the nonlinear dynamics of the homogeneous three-wave interaction may be reduced to [24,25,30,31]…”

Plasma Physics in Strong Field Regimes

“…This system of equations has been studied extensively in the literature. For the homogeneous problem, where the spatial derivatives are zero, the equations become a system of nonlinear ODEs, and the general solution is given by the Jacobi elliptic functions (Jurkus and Robson, 1960;Armstrong et al, 1962). Similarly, in one dimension, the steady state problem, where the time derivatives are zero, can also be solved in terms of the Jacobi elliptic functions (Harvey and Schmidt, 1975).…”

“…where R = Γ 2 /(ω 1 ω 2 ω 3 ) has the units of frequency. Since S 2 , S 3 > 0 are constants, the above equation can be solved in terms of the Jacobi elliptic function (Jurkus and Robson, 1960). To put Eq.…”