Kinetic equation for nonlinear resonant wave-particle interaction

Resonant Wave-Particle Interaction in Nonuniform Plasmas

The appearance of resonant-particle effects in the linear dynamics of electron waves in a plasma whose electrons are trapped in a potential trough is discussed and conditions for the characteristic times involved are derived. For the special case of a parabolic potential trough it is shown that, within a limited time interval, a strong resonant effect may occur, due to the interaction of a wave...

Exact solutions of the 3-wave resonant interaction equation

The Darboux–Dressing Transformations are applied to the Lax pair associated to the system of nonlinear equations describing the resonant interaction of three waves in 1+1 dimensions. We display explicit solutions featuring localized waves whose profile vanishes at the spacial boundary |x| = ∞, and which are not pure soliton solutions. These solutions depend on an arbitrary function and allow to...

Effect of nonlinear wave–particle interaction on electron-cyclotron absorption

We perform a self-consistent analysis of the nonlinear interaction of magnetized plasmas with electron-cyclotron (EC) waves. A closed set of equations is derived, which consists of the relativistic equations of motion under the wave field and the wave equation for the vector potential. The plasma is described in terms of ensembles of electrons which collectively determine the evolution of the w...

Forced Vibrations for a Nonlinear Wave Equation

Nonlinear wave evolution equation for critical layers.

Recent studies of the evolution of weakly nonlinear long waves in shear flows have revealed that when the wave field contains a critical layer, a new nonlinear wave equation is needed to describe the wave evolution. This equation is of the same type as the well-known Korteweg-de Vries equation but has a more complicated nonlinear structure. Our main interest is in the steady solitary wave solut...