Related papers: New photonic conservation laws in parametric nonli…
Symmetries and conservation laws are studied for two classes of physically and analytically interesting radial wave equations with power nonlinearities in multi-dimensions. The results consist of two main classifications: all symmetries of…
Energy conservation imposes fundamental bounds on the polarizabilities of nanoparticles (NPs). While such bounds are well established for isotropic and bianisotropic NPs, they remain unexplored for magneto-optical NPs. Here, we derive the…
Classifications of symmetries and conservation laws are presented for a variety of physically and analytically interesting wave equations with power onlinearities in n spatial dimensions: a radial hyperbolic equation, a radial Schrodinger…
Symmetries and conservation laws are studied for a generalized Westervelt equation which is a nonlinear partial differential equation modelling the propagation of sound waves in a compressible medium. This nonlinear wave equation is widely…
Time dependent systems in general do not conserve photons nor do they conserve energy. However when parity time symmetry holds Maxwells equations can sometimes both conserve photon number and energy. Here we show that photon conservation is…
Conservation laws are computed for various nonlinear partial differential equations that arise in elasticity and acoustics. Using a scaling homogeneity approach, conservation laws are established for two models describing shear wave…
All low-order conservation laws are found for a general class of nonlinear wave equations in one dimension with linear damping which is allowed to be time-dependent. Such equations arise in numerous physical applications and have attracted…
According to this principle (EEP), in order that the local physical laws cannot change, after changes of velocity and potentials of a measuring system, the relativistic changes of any particle and any stationary radiation (like those used…
Based on the reciprocity theorem, we put forward a generalized parametric space for an arbitrary transfer matrix with parity time (PT) symmetry. Through this space, one can extract complete information involving PT phases, reflectances,…
Conservation laws are discussed in conjunction with quantum-mechanical indeterminacies of the corresponding observables. The considered examples show that the connections between energy and its indeterminacy may be quite intricate. The…
A class of generalized nonlinear p-Laplacian evolution equations is studied. These equations model radial diffusion-reaction processes in $n\geq 1$ dimensions, where the diffusivity depends on the gradient of the flow. For this class, all…
Symmetry plays fundamental role in physics and the nature of symmetry changes in non-Hermitian physics. Here the symmetry-protected scattering in non-Hermitian linear systems is investigated by employing the discrete symmetries that…
In understanding the world of matter, the introduction of symmetry principles following experimentation or using the predictive power of symmetry principles to guide experimentation is most profound. The conservation of energy, linear…
In this paper we present a novel framework for obtaining high-order numerical methods for scalar conservation laws in one-space dimension for both the homogeneous and non-homogeneous case. The numerical schemes for these two settings are…
We report a new energy conservation law for time-harmonic electromagnetic fields, which is valid for an arbitrary medium. In contrast to the well-established Poynting theorem for time-harmonic fields, the real part of the new energy…
A complete classification of all low-order conservation laws is carried out for a system of coupled semilinear wave equations which is a natural two-component generalization of the nonlinear Klein-Gordon equation. The conserved quantities…
For the hyperbolic system of quasilinear first-order partial differential equations, linearizable by hodograph transformation, the conservation laws are used to solve the Cauchy problem. The equivalence of the initial problem for…
The analysis of symmetries is extremely useful across science. In Physics, symmetries are used to derive conservation laws and selection rules for transitions in interacting systems. In the early days of nonlinear optics (NLO), symmetries…
In the past decade, the concept of parity-time ($\mathcal{PT}$) symmetry, originally introduced in non-Hermitian extensions of quantum mechanical theories, has come into thinking of photonics, providing a fertile ground for studying,…
Conservation principles are essential to describe and quantify dynamical processes in all areas of physics. Classically, a conservation law holds because the description of reality can be considered independent of an observation…