We show a family of virial-type identities for the Schrödinger and wave equations with electromagnetic potentials. As a consequence, some weak dispersive inequalities in space dimension n ≥ 3, involving Morawetz and smoothing estimates, are proved; finally, we apply them to prove Strichartz inequalities for the wave equation with a non-trapping electromagnetic potential with almost Coulomb decay.

We study the dispersive character for waves on the one-dimensional free surface of an infinitely deep perfect fluid under the influence of surface tension. The main result state that, on average in time, the solution of the water-wave problem gains locally 1/4 derivative of smoothness in the spatial variable, compared to the initial state. The regularizing effect is a direct consequence of disp...

We show a family of virial-type identities for the Schrödinger and wave equations with electromagnetic potentials. As a consequence, some weak dispersive inequalities in space dimension n ≥ 3, involving Morawetz and smoothing estimates, are proved; finally, we apply them to prove Strichartz inequalities for the wave equation with a non-trapping electromagnetic potential with almost Coulomb decay.

In this paper, the two-dimensional Benney system describing long wave propagation of a finite depth fluid motion and the multi-dimensional Russo-Smereka kinetic equation describing a bubbly flow are considered. The Hamiltonian approach established by J. Gibbons for the one-dimensional Vlasov kinetic equation is extended to a multi-dimensional case. A local Hamiltonian structure associated with ...

With an extended mapping approach and a linear variable separation approach, a series of solutions (including the Weierstrass elliptic function solutions, solitary wave solutions, periodic wave solutions and rational function solutions) of the (2+1)-dimensional modified dispersive water-wave system (MDWW) is derived. Based on the derived solutions and using some multi-valued functions, we find ...

Undular bores and shocks generated by dam-break flows or tsunamis are examined considering nonhydrostatic pressure and dispersive effects in oneand two-horizontal-dimensional space. The fully nonlinear Boussinesq-type equations based on a weakly nonhydrostatic pressure assumption are chosen as the governing equations. The equation set is solved by a fourth-order accurate finite-volume method wi...

Here we consider the nonlinear evolution of Alfvén waves that have been excited by gravitational waves from merging binary pulsars. We derive a wave equation for strongly nonlinear and dispersive Alfvén waves. Due to the weak dispersion of the Alfvén waves, significant wave steepening can occur, which in turn implies strong harmonic generation. We find that the harmonic generation is saturated ...

The auxiliary differential equation finite-difference time-domain method for modeling electromagnetic wave propagation in dispersive nonlinear materials is applied to problems where the electric field is not constrained to a single vector component. A full-vector Maxwell's equations solution incorporating multiple-pole linear Lorentz, nonlinear Kerr, and nonlinear Raman polarizations is present...

We consider a generalized hyperelastic-rod wave equation (or generalized Camassa– Holm equation) describing nonlinear dispersive waves in compressible hyperelastic rods. We establish existence of a strongly continuous semigroup of global weak solutions for any initial data from H1(R). We also present a “weak equals strong”uniqueness result.

We consider a weakly dissipative hyperelastic-rod wave equation (or weakly dissipative Camassa–Holm equation) describing nonlinear dispersive dissipative waves in compressible hyperelastic rods. By fixed a smooth solution, we establish the existence of a strongly continuous semigroup of global weak solutions for any initial perturbation from H1(R). In particular, the supersonic solitary shock w...