Space and time solution for two coupled intensity deviations from a stationary nonlinear state

Details Space and time solution for two coupled intensity deviations from a stationary nonlinear state Space and time solution for two coupled intensity deviations from a stationary nonlinear state

Oct 1979

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979phys...20..352w&link_type=abstract

(National Swedish Board for Energy Source Development, Nobelstiftelsen, Nordisk Institut for Teoretisk Atomfysik, and Chalmers T

Statistics

Applications

3

Nonlinear Systems, Plasma Waves, Volterra Equations, Wave Interaction, Cauchy Problem, Fourier Analysis, Time Dependence, Wave Equations

Scientific paper

Coupled evolution equations are studied with a view to describing, for example, the stimulated scattering processes, which have been encountered frequently in recent laser-plasma experiments and various astrophysical applications. In the present paper we investigate some properties of a generalized form of the so called Volterra equations in two independent variables: time and one space coordinate. It is shown that this system of equations can be used to describe the interaction of two waves propagating in a nonlinear medium, such as a plasma, by means of a coupling to a strongly damped mode. It is also shown that under certain circumstances a stationary solution of the Volterra type equations exists. The evolution of small deviations from the stationary state for given arbitrary initial distribution of the variables, is examined in terms of certain integral representations. Applications to some generalized problems of mode competition in various physical systems are indicated.

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