Some contributions to the study of nonlinear dispersive wave phenomena in plasmas
Abstract
For a number of nonlinear evolution equations of physical significance it is shown that certain nonstationary similarity solutions exist and they can be expressed in terms of various Painleve transcendents if and only if the associated eigenvalue (scattering) operator is of second differential order. This result may be used as a test for the nature of the appropriate eigenvalue operator associated with a given nonlinear evolution equation. The problem of accounting for dissipative processes in the nonlinear interaction of dispersive waves is studied. A result of the investigation enables us to conclude that the solution to the problem of the evolution in time of three coherently interacting waves for which the linear dissipations are different corresponds to a class of transcendental functions for which the singularities of the general solution are of more complicated nature than those of the third Painleve transcendent.
 Publication:

Ph.D. Thesis
 Pub Date:
 May 1977
 Bibcode:
 1977PhDT.........9N
 Keywords:

 Nonlinear Equations;
 Plasma Physics;
 Transcendental Functions;
 Wave Dispersion;
 Wave Interaction;
 Coherence;
 Differential Equations;
 Eigenvalues;
 Energy Dissipation;
 Evolution (Development);
 Scattering;
 Singularity (Mathematics);
 Plasma Physics