This work continues our studies of nonlinear evolution of a system of wavepackets. We study a wave propagation governed by a nonlinear system of hyperbolic PDE's with constant coefficients with the initial data being a multi-wavepacket. By definition a general wavepacket has a well defined principal wave vector, and, as we proved in previous works, the nonlinear dynamics preserves systems of wa...

This work continues our studies of nonlinear evolution of a system of wavepackets. We study a wave propagation governed by a nonlinear system of hyperbolic PDE's with constant coefficients with the initial data being a multi-wavepacket. By definition a general wavepacket has a well defined principal wave vector, and, as we proved in previous works, the nonlinear dynamics preserves systems of wa...

The magnetic energy of nonlinear Alfvén waves in compressible plasmas may be ponderomotively coupled only to ion-acoustic quasi-modes which modulate the wave phase velocity and cause wave-front steepening. In the collisionless plasma with β 6= 0, the dynamics of nonlinear Alfvén wave is also affected by the resonant particle-wave interactions. Upon relatively rapid evolution (compared to the pa...

A third-order asymptotic solution in Lagrangian description for nonlinear water waves propagating over a sloping beach is derived. The particle trajectories are obtained as a function of the nonlinear ordering parameter ε and the bottom slope α to the third order of perturbation. A new relationship between the wave velocity and the motions of particles at the free surface profile in the waves p...

We study the nonlinear dynamics of particle acceleration in solar ares by analyzing the time series of various quasi-periodic radio signatures during ares. In particular we present the radio and hard X-ray data of 3 ares which support the following tentative conclusions: 1) Particle acceleration and injection into magnetic loops occurs intrinsically in a pulsed mode (with a typical period of 1-...

Moving Particle Semi-implicit (MPS) which is a meshless and full Lagrangian method is employed to simulate nonlinear hydrodynamic behavior in a wide variety of engineering application including free surface water waves. In the present study, a numerical particle-based model is developed by the authors using MPS method to simulate different wave problems in the coastal waters. In this model flui...