相关论文: Resolution of a shock in hyperbolic systems modifi…

The structure of steady plane-parallel radiative shock waves propagating through the hydrogen gas undergoing partial ionization and excitation of bound atomic states is investigated in terms of the self-consistent solution of the equations…

The piston shock problem is a prototypical example of strongly nonlinear fluid flow that enables the experimental exploration of fluid dynamics in extreme regimes. Here we investigate this problem for a nominally dissipationless, superfluid…

We investigate superdiffusion for stochastic processes generated by nonuniformly hyperbolic system models, in terms of the convergence of rescaled distributions to the normal distribution following the abnormal central limit theorem, which…

We provide a classification of the possible flow of two-component Bose-Einstein condensates evolving from initially discontinuous profiles. We consider the situation where the dynamics can be reduced to the consideration of a single…

We introduce and systematically investigate the generation of dispersive shock waves, which arise naturally in physical settings such as optical waveguide arrays and superfluids confined within optical lattices. The underlying physically…

The existence of ``dispersion-managed solitons'', i.e., stable pulsating solitary-wave solutions to the nonlinear Schr\"{o}dinger equation with periodically modulated and sign-variable dispersion is now well known in nonlinear optics. Our…

In this paper, we consider a coupled PDE system describing phase separation and damage phenomena in elastically stressed alloys in the presence of inertial effects. The material is considered on a bounded Lipschitz domain with mixed…

Propagation of extremely short pulses of electromagnetic field (electromagnetic spikes) is considered in the framework of the total Maxwell-Duffing model where anharmonic oscillators with cubic nonlinearities (Duffing model) represent the…

The oblique collisions and dynamical interference patterns of two-dimensional dispersive shock waves are studied numerically and analytically via the temporal dynamics induced by wedge-shaped initial conditions for the…

A theoretical investigation has been made to study the cylindrical and spherical electron-acoustic shock waves (EASWs) in an unmagnetized, collisionless degenerate quantum plasma system containing two distinct groups of electrons (one…

This paper studies the stability and large-time behavior of the three-dimensional (3-D) Boltzmann equation near shock profiles. We prove the nonlinear stability of the composite wave consisting of two shock profiles under general…

This paper considers a class of non-local equations that are weakly dispersive perturbations of the inviscid Burgers equation, which includes the Fornberg-Whitham equation as a special case. We precise the known results on finite time…

The paper investigates shock-induced vortical flows within inhomogeneous media of nonuniform thermodynamic properties. Numerical simulations are performed using an Eularian type mathematical model for compressible multi-component flow…

We study the critical behaviour of solutions to weakly dispersive Hamiltonian systems considered as perturbations of elliptic and hyperbolic systems of hydrodynamic type with two components. We argue that near the critical point of gradient…

Acoustic perturbations to stellar envelopes can lead to the formation of weak shock waves via nonlinear wave-steepening. Close to the stellar surface, the weak shock wave increases in strength and can potentially lead to the expulsion of…

A regularized Boussinesq equation is studied as a dispersive, long-wave (quasicontinuum) approximation of the Fermi-Pasta-Ulam lattice with a general cubic interaction force. Explicit periodic traveling wave solutions in terms of Jacobi…

Short-wave perturbations in a relaxing medium, governed by a special reduction of the Ostrovsky evolution equation, and later derived by Whitham, are studied using the gradient-holonomic integrability algorithm.The bi-Hamiltonicity and…

Strong non-relativistic shocks are known to accelerate particles up to relativistic energies. However, for Diffusive Shock Acceleration electrons must have a highly suprathermal energy, implying a need for very efficient pre-acceleration.…

We show existence of small solitary and periodic traveling-wave solutions in Sobolev spaces ${\mathrm{H}^s}$, ${ s > 0 }$, to a class of nonlinear, dispersive evolution equations of the form \begin{equation*} u_t + \left(Lu+ n(u)\right)_x =…

In this article we derive rigorously a nonlinear, steady, bifurcation through spectral bifurcation (i.e., eigenvalues of the linearized equation crossing the imaginary axis) for a class of hyperbolic-parabolic model in a strip. This is…