329 citations · 5.2k across the 203 of their papers we have counts for
68 papers · 1 filter
Twisted curve geometry underlying topological invariants
Radha Balakrishnan, Rossen Dandoloff, Avadh Saxena
Topological invariants such as winding numbers and linking numbers appear as charges of topological solitons in diverse nonlinear physical systems described by a unit vector field…
Uniform Bose-Einstein Condensates as Kovaton solutions of the Gross-Pitaevskii Equation through a Reverse-Engineered Potential
Fred Cooper, Avinash Khare, John F. Dawson +2
In this work, we consider a ``reverse-engineering'' approach to construct confining potentials that support exact, constant density kovaton solutions to the classical Gross-Pitaevs…
Nonlocal Superposed Solutions II: Coupled Nonlinear Equations
Avinash Khare, Avadh Saxena
We obtain novel periodic as well as hyperbolic solutions of an Ablowitz-Musslimani variant of the coupled nonlocal, nonlinear Schrödinger equation (NLS) as well as a coupled nonloc…
Kink Solutions With Power Law Tails
Avinash Khare, Avadh Saxena
We present a comprehensive review about the various facets of kink solutions with a power law tail which have received considerable attention during the last few years. This area o…
Novel Superposed Kinklike and Pulselike Solutions for Several Nonlocal Nonlinear Equations
Avinash Khare, Avadh Saxena
We show that a number of nonlocal nonlinear equations including the Ablowitz-Musslimani and the Yang variant of the nonlocal nonlinear Schröd-inger (NLS) equation, nonlocal modifie…
Stability of exact solutions of the -dimensional nonlinear Schrödinger equation with arbitrary nonlinearity parameter
Fred Cooper, Avinash Khare, Efstathios G. Charalampidis +2
In this work, we consider the nonlinear Schrödinger equation (NLSE) in dimensions with arbitrary nonlinearity exponent in the presence of an external confining potential.…
Superposed Hyperbolic Kink and Pulse Solutions of Coupled , NLS and MKdV Equations
Avinash Khare, Avadh Saxena
We obtain novel solutions of a coupled , a coupled nonlinear Schrödinger (NLS) and a coupled modified Korteweg de Vries (MKdV) model which can be re-expressed as a linear supe…
Novel Superposed Kink and Pulse Solutions for , MKdV, NLS and Other Nonlinear Equations
Avinash Khare, Avadh Saxena
We show that a number of nonlinear equations including symmetric as well as asymmetric , modified Korteweg de Vries (MKdV), mixed KdV-MKdV, nonlinear Schrödinger (NLS), quadra…
Measurement and Memory in the Periodically Driven Complex Ginzburg-Landau equation
T. Mithun, P. G. Kevrekidis, A. Saxena +1
In the present work we illustrate that classical but nonlinear systems may possess features reminiscent of quantum ones, such as memory, upon suitable external perturbation. As our…
Novel Deformation Function Creating or Destroying any Number of Even Kink Solutions
Avinash Khare, Avadh Saxena
We present a one-parameter family of deformation functions which have novel properties. Firstly, the deformation function is its own inverse. We show that a class of potenti…
Stability of exact solutions of a nonlocal and nonlinear Schrödinger equation with arbitrary nonlinearity
Efstathios G. Charalampidis, Fred Cooper, Avinash Khare +2
This work focuses on the study of solitary wave solutions to a nonlocal, nonlinear Schrödinger system in + dimensions with arbitrary nonlinearity parameter . Although the…
Explicit Kink Solutions in Several One-Parameter Family of Higher Order Field Theory Models
Avinash Khare, Ayhan Duzgun, Avadh Saxena
We present several one-parameter family of higher order field theory models some of which admit explicit kink solutions with an exponential tail while others admit explicit kink so…
Solitary wave solutions of the 2+1 and 3+1 dimensional nonlinear Dirac equation constrained to planar and space curves
Fred Cooper, Avinash Khare, Avadh Saxena
We study the effect of curvature and torsion on the solitons of the nonlinear Dirac equation considered on planar and space curves. Since the spin connection is zero for the curves…
Behavior of solitary waves of coupled nonlinear Schrödinger equations subjected to complex external periodic potentials with anti- symmetry
Efstathios G. Charalampidis, Fred Cooper, John F. Dawson +2
We discuss the response of both moving and trapped solitary wave solutions of a nonlinear two-component nonlinear Schrödinger system in 1+1 dimensions to an anti- ext…
Stability and response of trapped solitary wave solutions of coupled nonlinear Schrödinger equations in an external, - and supersymmetric potential
Efstathios G. Charalampidis, John F. Dawson, Fred Cooper +2
We present trapped solitary wave solutions of a coupled nonlinear Schrödinger system in + dimensions in the presence of an external, supersymmetric and complex …
Nonlinearity and Topology
A. Saxena, P. G. Kevrekidis, J. Cuevas-Maraver
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-E…
Parametrically driven nonlinear Dirac equation with arbitrary nonlinearity
Fred Cooper, Avinash Khare, Niurka R. Quintero +3
The damped and parametrically driven nonlinear Dirac equation with arbitrary nonlinearity parameter is analyzed, when the external force is periodic in space and given by $f(x)…
Logarithmic Potential with Super-Super-Exponential Kink Profiles and Tails
Avinash Khare, Avadh Saxena
We consider a novel one dimensional model of a logarithmic potential which has super-super-exponential kink profiles as well as kink tails. We provide analytic kink solutions of th…
Wide Class of Logarithmic Potentials with Power-Tower Kink Tails
Avinash Khare, Avadh Saxena
We present a wide class of potentials which admit kinks and corresponding mirror kinks with either a power law or an exponential tail at the two extreme ends and a power-tower form…
A model field theory with potential: Kinks with super-exponential profiles
Pradeep Kumar, Avinash Khare, Avadh Saxena
We study a (1+1)-dimensional field theory based on potential. There are three degenerate minima at and . There are novel, asymmetric kink solutions of t…
Connections Between Complex PT-Invariant Solutions and Complex Periodic Solutions of Several Nonlinear Equations
Avinash Khare, Avadh Saxena
We point out novel connections between complex PT-invariant solutions of several nonlinear equations such as , , sine-Gordon, hyperbolic sine-Gordon, double sine-Gordon,…
Speed-of-light pulses in a nonlinear Weyl equation
J. Cuevas-Maraver, P. G. Kevrekidis, F. G. Mertens +1
We introduce a prototypical nonlinear Weyl equation, motivated by recent developments in massless Dirac fermions, topological semimetals and photonics. We study the dynamics of its…
Solitary waves in the Nonlinear Dirac Equation
J. Cuevas-Maraver, N. Boussaïd, A. Comech +3
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-interacti…
Response of exact solutions of the nonlinear Schrodinger equation to small perturbations in a class of complex external potentials having supersymmetry and parity-time symmetry
Fred Cooper, John F. Dawson, Franz G. Mertens +5
We discuss the effect of small perturbation on nodeless solutions of the nonlinear \Schrodinger\ equation in 1+1 dimensions in an external complex potential derivable from a parity…