SAXENA , Avadh

The interplay of nonlinearity and topology results in many novel and emergent properties across a number of physical systems such as chiral magnets, nematic liquid crystals, Bose-Einstein condensates, photonics, high energy physics, etc. It also results in a wide variety of topological defects such as solitons, vortices, skyrmions, merons,...

In the present work, we introduce a discrete formulation of the nonlinear Dirac equation in the form of a discretization of the Gross – Neveu model. The motivation for this discrete model proposal is both computational (near the continuum limit) and theoretical (using the understanding of the anti-con- tinuum limit of vanishing coupling)....

We provide a systematic analysis of a prototypical nonlinear oscillator system respecting PT symmetry i.e., one of them has gain and the other an equal and opposite amount of loss. Starting from the linear limit of the system, we extend considerations to the nonlinear case for both soft and hard cubic nonlinearities identifying symmetric and...

In the present work, we explore a nonlinear Dirac equation motivated as the continuum limit of a binary waveguide array model. We approach the problem both from a near-continuum perspective as well as from a highly discrete one. Starting from the former, we see that the continuum Dirac solitons can be continued for all values of the...

In this work, we explore a massless nonlinear Dirac equation, i.e., a nonlinear Weyl equation. We study the dynamics of its pulse solutions and find that a localized one-hump initial condition splits into a localized two hump pulse, while an associated phase structure emerges in suitable components of the spinor field. For times larger than a...

In the present work, we combine the notion of parity-time (PT ) symmetry with that of supersymmetry (SUSY) for a prototypical case example with a complex potential that is related by SUSY to the so-called P¨oschl-Teller potential which is real. Not only are we able to identify and numerically confirm the eigenvalues of the relevant problem, but...

N.R.Q. acknowledges financial support from the Humboldt Foundation through Research Fellowship for Experienced Researchers SPA 1146358 STP (Germany)

In the present work, we explore the case of a general PT -symmetric dimer in the context of two both linearly and nonlinearly coupled cubic oscillators. To obtain an analytical handle on the system, we first explore the rotating wave approximation converting it into a discrete nonlinear Schr¨odinger type dimer. In the latter context, the...

We consider the nonlinear Dirac equation in 1 + 1 dimension with scalar-scalar self interaction g2κ+1(Ψ¯¯¯Ψ)κ+1 and with mass m. Using the exact analytic form for rest frame solitary waves of the form Ψ(x,t)=ψ(x)e−iωt for arbitrary κ, we discuss the validity of various approaches to understanding stability that were successful for the nonlinear...

We explore a prototypical two-dimensional massive model of the nonlinear Dirac type and examine its solitary wave and vortex solutions. In addition to identifying the stationary states, we provide a systematic spectral stability analysis, illustrating the potential of spinor solutions to be neutrally stable in a wide parametric interval of...

We consider nonlinear Dirac equations (NLDE's) in the 1+1 dimension with scalar-scalar self-interaction g2κ+1(Ψ¯¯¯Ψ)κ+1 in the presence of various external electromagnetic fields. We find exact solutions for special external fields and we study the behavior of solitary-wave solutions to the NLDE in the presence of a wide variety of fields in a...

We consider the nonlinear Schrödinger equation (NLSE) in 1+1 dimension with scalar-scalar self-interaction g2κ+1(ψ☆ψ)κ+1 in the presence of the external forcing terms of the form re−i(kx+θ)−δψ. We find new exact solutions for this problem and show that the solitary wave momentum is conserved in a moving frame where vk=2k. These new exact...

In the present work, we give a comparative summary of different recent contributions to the theme of the linear stability and nonlinear dynamics of solitary waves in the nonlinear Dirac equation in the form of the Gross-Neveu model. We indicate some of the key controversial statements in publications within the past few years and we attempt to...

We consider the massless nonlinear Dirac (NLD) equation in 1+1 dimension with scalar­ scalar self-interaction g² ̸ 2 (ψ ψ)² in the presence of three externa! electromagnetic real potentials V(x), a potential barrier, a constant potential, and a potential well. By solving numerically the NLD equation, we find different scenarios depending on...

In the present work, we consider the existence, stability, and dynamics of solitary waves in the nonlinear Dirac equation. We start by introducing the Soler model of self-interacting spinors, and discuss its localized waveforms in one, two, and three spatial dimensions and the equations they satisfy. We present the associ- ated explicit...

We consider the nonlinear Dirac (NLD) equation in 1+1 dimension with scalar-scalar selfinteraction in the presence of external forces as well as damping of the form f (x, t) - ιμγͦψ, where both f and ψ are two-component spinors. We develop an approximate variational approach using collective coordinates (CC) for studying the time dependent...

We consider the nonlinear Dirac (NLD) equation in 1+1 dimension with scalar-scalar selfinteraction in the presence of external forces as well as damping of the form γͦf(x-t) - ιμγͦψ, where both f, {fj = rieiKjx} and ψ are two-component spinors. We develop an approximate variational approach using collective coordinates (CC) for studying the...

The damped and parametrically driven nonlinear Dirac equation with arbitrary nonlinearity parameter κ is analyzed, when the external force is periodic in space and given by f(x) = r cos(Kx), both numerically and in a variational approximation using five collective coordinates (time dependent shape parameters of the wave function). Our...

In the present work, we consider a prototypical example of a PT -symmetric Dirac model. We discuss the underlying linear limit of the model and identify the threshold of the PT -phase transition in an analytical form. We then focus on the examination of the nonlinear model. We consider the continuation in the PT -symmetric model of the...

We discuss the effect of small perturbation on nodeless solutions of the nonlinear Schrödinger equation in 1 + 1 dimensions in an external complex potential derivable from a parity-time symmetric superpotential that was considered earlier (Kevrekidis et al 2015 Phys. Rev. E 92 042901). In particular, we consider the nonlinear partial...

Neutron capture cross section measurements on 155Gd and 157Gd were performed using the time-of-flight technique at the n_TOF facility at CERN on isotopically enriched samples. The measurements were carried out in the n_TOF experimental area EAR1, at 185 m from the neutron source, with an array of 4 C6D6 liquid scintillation detectors. At a...