Search results for "waves"
showing 10 items of 1766 documents
Degenerate determinant representation of solutions of the NLS equation, higher Peregrine breathers and multi-rogue waves.
2012
We present a new representation of solutions of the focusing NLS equation as a quotient of two determinants. This work is based on a recent paper in which we have constructed a multi-parametric family of this equation in terms of wronskians. This formulation was written in terms of a limit involving a parameter. Here we give a very compact formulation without presence of a limit. This is a completely new result which gives a very efficient procedure to construct families of quasi-rational solutions of the NLS equation. With this method, we construct Peregrine breathers of orders N=4 to 7 and multi-rogue waves associated by deformation of parameters.
Solutions to the NLS equation : differential relations and their different representations
2020
Solutions to the focusing nonlinear Schrödinger equation (NLS) of order N depending on 2N − 2 real parameters in terms of wronskians and Fredholm determinants are given. These solutions give families of quasirational solutions to the NLS equation denoted by vN and have been explicitly constructed until order N = 13. These solutions appear as deformations of the Peregrine breather PN as they can be obtained when all parameters are equal to 0. These quasi rational solutions can be expressed as a quotient of two polynomials of degree N (N + 1) in the variables x and t and the maximum of the modulus of the Peregrine breather of order N is equal to 2N + 1. Here we give some relations between sol…
Families of solutions of order nine to the NLS equation with sixteen parameters
2015
We construct new deformations of the Peregrine breather (P9) of order 9 with 16 real parameters. With this method, we obtain explicitly new families of quasi-rational solutions to the NLS equation in terms of a product of an exponential depending on t by a ratio of two polynomials of degree 90 in x and t; when all the parameters are equal to 0, we recover the classical P9 breather. We construct new patterns of different types of rogue waves as triangular configurations of 45 peaks as well as rings and concentric rings.
Patterns of deformations of P 3 and P 4 breathers solutions to the NLS equation
2016
In this article, one gives a classification of the solutions to the one dimensional nonlinear focusing Schrödinger equation (NLS) by considering the modulus of the solutions in the (x, t) plan in the cases of orders 3 and 4. For this, we use a representation of solutions to NLS equation as a quotient of two determinants by an exponential depending on t. This formulation gives in the case of the order 3 and 4, solutions with respectively 4 and 6 parameters. With this method, beside Peregrine breathers, we construct all characteristic patterns for the modulus of solutions, like triangular configurations, ring and others.
Tenth Peregrine breather solution of the NLS equation.
2012
We go on in this paper, in the study of the solutions of the focusing NLS equation. With a new representation given in a preceding paper, a very compact formulation without limit as a quotient of two determinants, we construct the Peregrine breather of order N=10. The explicit analytical expression of the Akhmediev's solution is completely given.
Tenth order solutions to the NLS equation with eighteen parameters
2015
We present here new solutions of the focusing one dimensional non linear Schrödinger equation which appear as deformations of the Peregrine breather of order 10 with 18 real parameters. With this method, we obtain new families of quasi-rational solutions of the NLS equation, and we obtain explicit quotients of polynomial of degree 110 in x and t by a product of an exponential depending on t. We construct new patterns of different types of rogue waves and recover the triangular configurations as well as rings and concentric as found for the lower orders.
Nonlocal dispersion anomalies of Dyakonov-like surface waves at hyperbolic media interfaces
2016
Dyakonov-like surface waves (DSWs) propagating obliquely on an anisotropic nanostructure have been theoretically proved in a few cases including 2D photonic crystals and metal-insulator (MI) layered metamaterials. Up to now, the long-wavelength approximation has been employed in order to obtain effective parameters to be introduced in the Dyakonov equation, which is largely restricted to material inhomogeneities of a few nanometers when including metallic elements. Here, we explore DSWs propagating obliquely at the interface between an insulator and a hyperbolic metamaterial, the latter consisting of a 1D MI bandgap grating using realistic slab sizes. We found unexpected favorable condition…
Molecular polarizability of Si/Ge/GaAs semiconductors clusters
2004
The interacting induced dipole polarization model implemented in our program for the calculation of molecular polarizabilities (POLAR) is used for the calculation of the molecular dipole-dipole polarizability ${\overline{\overline{α}}}$. POLAR is tested with Si$_{n}$, Ge$_{n}$ and Ga$_{n}$As$_{m}$ small clusters. The polarizability is an important quantity for the identification of clusters with different numbers of atoms and even for the separation of isomers. The results for the polarizability are in agreement with reference calculations performed with our version of the program PAPID (polarisabilites atomiques par interactions dipolaires) and with reference computations from Dr. J.R. Che…
Effect of size and deformation on polarizabilities of carbon nanotubes from atomic increments
2004
The interacting induced-dipole polarization model implemented in program POLAR is used for the calculation of the polarizability α. The method is tested with single-wall carbon nanotubes (SWNTs) as a function of radius and elliptical deformation. This work gives a partial success with the application of POLAR when compared with reference calculations performed with program PAPID. α follows a simple law. PAPID differentiates more effectively than POLAR among SWNTs with increasing radial deformation, a can be modified reversibly by external radial deformation. Different effective αeff are calculated for the atoms at the highest and lowest curvature sites. The difference between POLAR and PAPI…
Polarization Switching in Heterophase Nanostructures: PLZT Relaxor Ceramics
2005
The polarization switching is experimentally investigated in hot-pressed PLZT-x/65/35 ceramics with a lanthanum content from 5 to 12 at. %. The specific features in the temperature dependence of the polarization switching in a heterophase state are interpreted by analyzing the change in the switched charge measured over wide ranges of fields and temperatures. Particular emphasis is placed on the role of depolarization fields induced by interphase boundaries. A model of the evolution of polydomain nanostructures with a change in the temperature and in the response to an external field is considered. It is assumed that the low-temperature dielectric anomaly and the temperature hysteresis are …