Related papers: First-order continuum models for nonlinear dispers…
We study generic waves without rotational symmetry in (2+1) - dimensional noncommutative scalar field theory. In the representation chosen, the radial coordinate is naturally rendered discrete. Nonlocality along this coordinate, induced by…
The one-dimensional piston shock problem is a classical result of shock wave theory. In this work, the analogous dispersive shock wave (DSW) problem for a dispersive fluid described by the nonlinear Schr\"odinger equation is analyzed.…
We consider dispersive optical shock waves in nonlocal nonlinear media. Experiments are performed using spatial beams in a thermal liquid cell, and results agree with a hydrodynamic theory of propagation.
Acoustic wave propagation in a one-dimensional waveguide connected with Helmholtz resonators is studied numerically. Finite amplitude waves and viscous boundary layers are considered. The model consists of two coupled evolution equations: a…
We model the expansion of an interacting atomic Bose-Einstein condensate in a disordered lattice with a nonlinear diffusion equation normally used for a variety of classical systems. We find approximate solutions of the diffusion equation…
We introduce and study a family of lattice equations which may be viewed either as a strongly nonlinear discrete extension of the Gardner equation, or a non-convex variant of the Lotka-Volterra chain. Their deceptively simple form supports…
We investigate the integrability of a class of 1+1 dimensional models describing nonlinear dispersive waves in continuous media, e.g. cylindrical compressible hyperelastic rods, shallow water waves, etc. The only completely integrable cases…
The main subject of this thesis rests on the study ---at different levels of description--- of instabilities in systems which are driven, i.e., maintained far from equilibrium by an external forcing. We focus here on two main classes,…
Dispersive waves in two-dimensional blocky materials with periodic microstructure made up of equal rigid units having polygonal centro-symmetric shape with mass and gyroscopic inertia, connected each other through homogeneous linear…
In this work, we propose a nonlinear stabilization technique for scalar conservation laws with implicit time stepping. The method relies on an artificial diffusion method, based on a graph-Laplacian operator. It is nonlinear, since it…
We show that an hyperbolic system with a mathematical entropy can be discretized with vectorial lattice Boltzmann schemes with the methodology of kinetic representation of the dual entropy. We test this approach for the shallow water…
It is the aim of the paper to present a new point of view on rotational elasticity in a nonlinear setting using orthogonal matrices. The proposed model, in the linear approximation, can be compared to the well known equilibrium equations of…
We experimentally investigate the impulsive shock propagation caused by an impact into vertically oriented 3D granular packings under gravity. We observe a crossover of wave propagation, from sound excitation at low impact to shock front…
Properties of solitary waves in pre-compressed Hertzian chains of particles are studied in the long wavelength limit using a well-known continuum model. Several main results are obtained by parameterizing the solitary waves in terms of…
We study the following family of evolutionary 1+1 PDEs that describe the balance between convection and stretching for small viscosity in the dynamics of 1D nonlinear waves in fluids: \[ m_t + \underbrace{um_x \}…
In this paper, we initiate the study of wave propagation in a recently proposed mathematical model for stretch-limited elastic strings. We consider the longitudinal motion of a simple class of uniform, semi-infinite, stretch-limited strings…
In this paper we present an improved lattice Boltzmann model for compressible Navier-Stokes system with high Mach number. The model is composed of three components: (i) the discrete-velocity-model by Watari and Tsutahara [Phys Rev E…
A model of local metastable states due to the pinning induces plastic deformations allows to describe the nonlinear I-V curves in sliding density waves -DW. With increasing the DW velocity v, the metastable states of decreasing lifetimes…
Parametric simultaneous solitary wave (simulton) excitations are shown possible in nonlinear lattices. Taking a one-dimensional diatomic lattice with a cubic potential as an example we consider the nonlinear coupling between the upper…
We provide a both qualitative and quantitative comparison among different approaches aimed to solve the problem of non-linear diffusive acceleration of particles at shocks. In particular, we show that state-of-the-art models (numerical,…