Related papers: Particles versus fields in PT-symmetrically deform…
The second-order differential equation describes harmonic oscillators, as well as currents in LCR circuits. This allows us to study oscillator systems by constructing electronic circuits. Likewise, one set of closed commutation relations…
We study integrable non-degenerate Monge-Ampere equations of Hirota type in 4D and demonstrate that their symmetry algebras have a distinguished graded structure, uniquely determining the equations. This is used to deform these heavenly…
We show that the ideas related to integrability and symmetry play an important role not only in the string T-duality story but also in its point particle counterpart. Applying those ideas, we find that the T-duality seems to be a more…
Despite its non-Hermitian nature, the transverse optical beam shift exhibits both real eigenvalues and non-orthogonal eigenstates. To explore this unexpected similarity to typical PT (parity-time)-symmetric systems, we first categorize the…
We present an inverse scattering approach to defects in classical integrable field theories. Integrability is proved systematically by constructing the generating function of the infinite set of modified integrals of motion. The…
We propose a new numerical technique for following the evolution of a self-gravitating collisionless system in general relativity. Matter is modeled as a scalar field obeying the coupled Klein-Gordon and Einstein equations. A phase space…
When we consider a differential equation $\Delta=0$ whose set of solutions is ${{\cal S}}_\Delta$, a Lie-point exact symmetry of this is a Lie-point invertible transformation $T$ such that $T({{\cal S}}_\Delta)={{\cal S}}_\Delta$, i.e. such…
In this article, we consider an interesting class of optical and other systems in which the interaction or coupling makes the systems to be $\cal{PT}$-symmetric. We aim to compare their dynamical behaviors with that of the usual $\cal{PT}$…
Second order integrals of motion for 3d quantum mechanical systems with position dependent masses (PDM) are classified. Namely, all PDM systems are specified which, in addition to their rotation invariance, admit at least one second order…
Polymer quantum mechanics has been studied as a simplified picture that reflects some of the key properties of Loop Quantum Gravity; however, while the fate of relativistic symmetries in Loop Quantum Gravity is still not established, it is…
The paper deals with the problem of integration of equations of motion in nonholonomic systems. By means of well-known theory of the differential equations with an invariant measure the new integrable systems are discovered. Among them…
An invertible field transformation is such that the old field variables correspond one-to-one to the new variables. As such, one may think that two systems that are related by an invertible transformation are physically equivalent. However,…
The Riemann-Hilbert problem associated with the integrable PDE is used as a nonlinear transformation of the nearly integrable PDE to the spectral space. The temporal evolution of the spectral data is derived with account for arbitrary…
We consider bright solitons supported by a symmetric inhomogeneous defocusing nonlinearity growing rapidly enough toward the periphery of the medium, combined with an antisymmetric gain-loss profile. Despite the absence of any symmetric…
We analyse some PT-symmetric oscillators with $T_{d}$ symmetry that depend on a potential parameter $g$. We calculate the eigenvalues and eigenfunctions for each irreducible representation and for a range of values of $g$. Pairs of…
A variational technique is established to deal with the Schrodinger equation with parity-time(PT) symmetric Gaussian complex potential. The method is extended to the linear and self-focusing and defocusing nonlinear cases. Some unusual…
Present PT-symmetry deals with broken and unbroken spectra of ML oscillator.
Several new proton-proton parity violation experiments are presently either being performed or are being prepared for execution in the near future. Similarly, a new measurement of the parity-violating gamma-ray asymmetry in polarized…
Symmetry, which describes invariance, is an eternal concern in mathematics and physics, especially in the investigation of solutions to the partial differential equation (PDE). A PDE's nonlocally related PDE systems provide excellent…
Simple deformations, with a parameter $\epsilon$, of classical $R$-matrices which follow from decomposition of appropriate Lie algebras, are considered. As a result nonstandard Lax representations for some well known integrable systems are…