相关论文: Gurevich-Zybin system

The relation between Gribov ambiguity and degeneracies in the symplectic structure of physical systems is analyzed. It is shown that, in finite-dimensional systems, the presence of Gribov ambiguities in regular constrained systems (those…

Terahertz high harmonic generation (THz HHG) is a common property of nonlinear systems. Recently it has been used to investigate fundamental principles that govern transport and nonlinear dynamics in novel quantum materials like graphene,…

Nonlinear phenomena are inherent in most systems in nature. Second or higher-order harmonic generations, three-wave and four-wave mixing are typical phenomena in nonlinear optics. To obtain a nonzero signal for second-harmonic generation in…

The paper introduces a new way to construct dissipative solutions to a second order variational wave equation. By a variable transformation, from the nonlinear PDE one obtains a semilinear hyperbolic system with sources. In contrast with…

Nonreciprocal devices that allow the light propagation in only one direction are indispensable in photonic circuits and emerging quantum technologies. Contemporary optical isolators and circulators, however, require large size or strong…

The classes of Monge-Amp\`ere systems, decomposable and bi-decomposable Monge-Amp\`ere systems, including equations for improper affine spheres and hypersurfaces of constant Gauss-Kronecker curvature are introduced. They are studied by the…

Weakly nonlinear analysis of resonant PDEs in recent literature has generated a number of resonant systems for slow evolution of the normal mode amplitudes that possess remarkable properties. Despite being infinite-dimensional Hamiltonian…

We study the bi-Hamiltonian structures for the hierarchy of a 3-component generalization of the Degasperis-Procesi (3-DP) equation. We show that all Hamiltonian functionals in the hierarchy are homogenous, and Hamiltonian functionals of the…

Using the bicomplex approach we discuss a noncommutative system in two--dimensional Euclidean space. It is described by an equation of motion which reduces to the ordinary sine--Gordon equation when the noncommutation parameter is removed,…

Recent advances in fundamental performance limits for power quantities based on Lagrange duality are proving to be a powerful theoretical tool for understanding electromagnetic wave phenomena. To date, however, in any approach seeking to…

In this paper, we develop a nested hybridizable discontinuous Galerkin (HDG) method to numerically solve the Maxwell's equations coupled with the hydrodynamic model for the conduction-band electrons in metals. By means of a static…

Continuous unitary transformations can be used to diagonalize or approximately diagonalize a given Hamiltonian. In the last four years, this method has been applied to a variety of models of condensed matter physics and field theory. With a…

We theoretically investigate second harmonic generation in extremely narrow, sub-wavelength semiconductor and dielectric waveguides. We discuss a novel guiding mechanism characterized by the inhibition of diffraction and the suppression of…

This research will examine the computational methods to calculate the nonlinear optical process of second harmonic generation (SHG) that will be hypothesized to be present during lithium ion insertion into silicon nanowires. First it will…

We study second and third harmonic generation in centrosymmetric semiconductors at visible and UV wavelengths in bulk and cavity environments. Second harmonic generation is due to a combination of symmetry breaking, the magnetic portion of…

Central issues of the Dirac constraint formalism are discussed in relation to the algorithmic methods of commutative algebra based on the Groebner basis techniques. For a wide class of finite dimensional polynomial degenerate Lagrangian…

We study several $3\times 3$ systems of conservation laws, arising in modeling of two phase flow with rough porous media and traffic flow with rough road condition. These systems share several features. The systems are of mixed type, with…

We investigate Second Harmonic Generation from individual silicon nanowires and study the influence of resonant optical modes on the far-field nonlinear emission. We find that the polarization of the Second Harmonic has a size-dependent…

Second-harmonic-generation (SHG) in centrosymmetric material such as Si(111) is usually understood either from the phenomenology theory or more recently using the Simplified Bond-Hyperpolarizability Model (SBHM) [G. D. Powell, J. F. Wang,…

We present three novel forms of the Monge-Ampere equation, which is used, e.g., in image processing and in reconstruction of mass transportation in the primordial Universe. The central role in this paper is played by our Fourier integral…