Laser evolution and plasma wave excitation by a relativistically intense short-pulse laser in underdense plasma are investigated in the broad pulse limit, including the effects of pulse steepening, frequency redshifting, and energy depletion. The nonlinear plasma wave phase velocity is shown to be significantly lower than the laser group velocity and further decreases as the pulse propagates ow...

Evolution of a Langmuir wave is studied numerically for finite amplitudes slightly above the threshold which separates damping from nondamping cases. Arrest of linear damping is found to be a second-order effect due to ballistic evolution of perturbations, resonant power transfer between field and particles, and organization of phase space into a positive slope for the average distribution func...

Massive stars can significantly modify the surrounding medium during their lifetime. When the stars explode as supernovae, the resulting shock wave expands within this modified medium and not within the interstellar medium. We explore the evolution of the medium around massive stars, and the expansion of the shock wave within this medium. We then apply these results to understanding the expansi...

This work studies the impact of wind on extreme wave events, by means of numerical analysis. A High Order Spectral Method (HOSM) is used to generate freak, or rogue waves, on the basis of modulational instability. Wave fields considered here are chosen to be unstable to two kinds of perturbations. The evolution of components during the propagation of the wave fields is presented. Their evolutio...

A numerical scheme for solving the time evolution of wave functions under the time-dependent Kohn-Sham (TDKS) equation has been developed. Since the effective Hamiltonian depends on the wave functions, the wave functions and the effective Hamiltonian should evolve consistently with each other. For this purpose, a self-consistent loop is required at every time step for solving the time evolution...

A generalized and improved G′/G -expansion method is proposed for finding more general type and new travelling wave solutions of nonlinear evolution equations. To illustrate the novelty and advantage of the proposed method, we solve the KdV equation, the Zakharov-KuznetsovBenjamin-Bona-Mahony ZKBBM equation and the strain wave equation in microstructured solids. Abundant exact travelling wave s...

The modified simple equation method is employed to find the exact traveling wave solutions involving parameters for nonlinear evolution equations namely, a diffusive predator-prey system, the Bogoyavlenskii equation, the generalized Fisher equation and the Burgers-Huxley equation. When these parameters are taken special values, the solitary wave solutions are derived from the exact traveling wa...

In this paper, the extended mapping method with symbolic computation is developed to obtain exact periodic wave solutions for nonlinear evolution equations arising in mathematical physics. Limit cases are studied and new solitary wave solutions and triangular periodic wave solutions are obtained. The method is applicable to a large variety of nonlinear partial differential equations, as long as...

We provide estimates for the error incurred when a wave field produced by a directional source localized within a given plane is approximated by decoupled evolution equations describing the portions of the field moving upward and downward. The evolution equations are either pseudodifferential or of Schrödinger type (i.e. the so-called paraxial approximation) although in the latter case we must ...

The nonlinear evolution of waves excited by the resonant interaction with energetic particles, just above the instability threshold, is shown to depend on the type of relaxation process that restores the unstable distribution function. When dynamical friction dominates over diffusion in the phase space region surrounding the wave-particle resonance, an explosive evolution of the wave is found t...