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The formation of extreme localizations in nonlinear dispersive media can be explained and described within the framework of nonlinear evolution equations, such as the nonlinear Schr\"odinger equation (NLS). Within the class of exact NLS…
Spatial characteristics of diffracted beams produced by the "fork" holograms from incident circular Lauerre-Gaussian modes are studied theoretically. The complex amplitude distribution of a diffracted beam is described by models of the…
We compare the Gram-Schmidt and covariant phase-space-basis-vector descriptions for three time-reversible harmonic oscillator problems, in two, three, and four phase-space dimensions respectively. The two-dimensional problem can be solved…
The emergence of the chimera state as counterintuitive spatial coexistence of synchronous and asynchronous regimes is addressed here in a continuum chemical oscillator system by implementing a relevant complex Ginzburg-Landau equation with…
Nondispersive wave packets in a fictitious time variable are calculated analytically for the field-free hydrogen atom. As is well known by means of the Kustaanheimo-Stiefel transformation the Coulomb problem can be converted into that of a…
Gamma-ray bursts are a complex, non-linear system that evolves very rapidly through stages of vastly different conditions. They evolve from scales of few hundred kilometers where they are very dense and hot to cold and tenuous on scales of…
This paper develops the basic sets of equations which lead to the conservation laws describing collisionless plasma shock waves. We discuss the evolution of shock waves by wave steepening, derive the Rankine-Hugoniot conditions for…
Spiral waves are striking self-organized coherent structures that organize spatio-temporal dynamics in dissipative, spatially extended systems. In this paper, we provide a conceptual approach to various properties of spiral waves. Rather…
Modeling the propagation of gravitational waves (GWs) through matter is complicated by the gauge freedom of linearized gravity in that once nonlinearities are taken into consideration, gauge artifacts can cause spurious acceleration of the…
The coherent state of a nonlinear oscillator having a nonlinear spectrum is constructed using Gazeau Klauder formalism. The weighting distribution and the Mandel parameter are studied. Details of the revival structure arising from different…
We study the variational principle over an Hilbert-Einstein like action for an extended geometry taking into account torsion and non-metricity. By extending the semi-Riemannian geometry, we obtain an effective energy-momentum tensor which…
The irreducible representations of the extended Galilean group are used to derive the symmetric and asymmetric wave equations. It is shown that among these equations only a new asymmetric wave equation is fundamental. By being fundamental…
Observation of low- and high-frequency backward waves in the nonlinear regime of the Buneman instability is reported. Intense low-frequency backward waves propagating in the direction opposite to the electron drift (with respect to the ion…
Internal waves, or waves that propagate within a stratified fluid, may break and cause mixing. While each individual mixing event may be small, collectively, internal wave breaking drive processes in the ocean that are critical to…
Researchers have developed hybrid Van der Pol Rayleigh Duffing type oscillators to model human induced forces; however, their analytical framework has largely relied on the Lindstedt Poincare perturbation method, energy balance approaches,…
The breaking of an approximate discrete symmetry, the final stages of a first order phase transition, or a post-inflationary biased probability distribution for scalar fields are possible cosmological scenarios characterized by the presence…
In this paper, we experimentally demonstrate reversible wavefront shaping through mimicking gravitational field. A gradient-index micro-structured optical waveguide with special refractive index profile was constructed whose effective index…
We study the wave equation in a bounded domain or on a compact Riemannian manifold with boundary. Assume that we are given the hyperbolic Neumann-to-Dirichlet map on the boundary corresponding to physical boundary measurements. We consider…
Gamma-Ray Burst (GRB) afterglows are well described by synchrotron emission from relativistic blast waves expanding into an external medium. The blast wave is believed to amplify the magnetic field and accelerate the electrons into a power…
We attempt to characterize irreversibility of a dynamical system from the existence of different forward and backward mathematical representations depending on the direction of the time arrow. Such different representations have been…