48 citations · 50 across the 16 of their papers we have counts for
20 papers
Hyperbolic, Trigonometric and Periodic Solutions of Local and Nonlocal Fokas-Lennels Equations
Avinash Khare, Avadh Saxena
We obtain a large number of exact hyperbolic, trigonometric, and periodic solutions in terms of Jacobi elliptic functions as well as algebraic solutions with a power law tail of th…
Two-Parameter Family of Nonlinear Dirac Equations With Scalar-Scalar plus Vector-Vector Interactions
Avinash Khare, Fred Cooper, John F. Dawson +1
We obtain exact solutions of the nonlinear Dirac equation in dimensions of the form for scalar-scalar (SS) plus vector-vector (VV) interaction with i…
Quantum geometric potential induced conformational transitions in elastic helical nanoribbons
Radha Balakrishnan, Rossen Dandoloff, Avadh Saxena
We consider an {\em elastic} helical nanoribbon that can take on various conformations, and study the effect of placing a quantum particle on its curved surface. Using a modified C…
Integrable motion of curves associated with the Fokas-Lenells equation and related spin system
R. Ramakrishnan, Sagardeep Talukdar, M. Lakshmanan +1
In this article, we study the gauge equivalence between the integrable Fokas- Lenells equation (FLE) and an associated spin equation through a gauge transformation and the zero cur…
Collective dynamics in a one-dimensional Heisenberg ferromagnetic spin chain
R. Arun, M. Lakshmanan, Avadh Saxena
We investigate the different oscillatory modes, namely, complete synchronization, inphase synchronization, antiphase synchronization and desynchronization in a one-dimensional anis…
One-Parameter Family of Elliptic Sine-Gordon Equations
Avinash Khare, Avadh Saxena
We introduce a continuous one-parameter family of elliptic sine-Gordon equations (SGE) characterized by the modulus of Jacobi elliptic functions and analyze some of…
Linear Superposition of Quadratic Functions in a Fifth Order KdV-Type Equation
Avinash Khare, Avadh Saxena
We show that a fifth order KdV-type equation admits several real as well as complex parity-time reversal or PT-invariant solutions with linear superposition of quadratic functions…
Some Novel Aspects of the Plane Pendulum in Classical Mechanics
Avinash Khare, Avadh Saxena
We obtain a novel connection between the exact solutions of the plane pendulum, hyperbolic plane pendulum and inverted plane pendulum equations as well as the static solutions of t…
Particle localization on helical nanoribbons: Quantum analog of the Coriolis effect
Radha Balakrishnan, Rossen Dandoloff, Victor Atanasov +1
We derive the Schrödinger equation for a particle confined to the surface of a normal and a binormal helical nanoribbon, obtain the quantum potentials induced by their respective c…
Solitons of the Symmetric -- Triple Well Model
Avinash Khare, Avadh Saxena
A symmetric -- model has recently attracted a lot of attention due to its usefulness in studying tunable phase transitions. We analyze the behavior of this model…
Programmable Exploration of Magnetic States in Lieb-Kagome Interpolated Lattices
Alejandro Lopez-Bezanilla, Pavel A. Dub, Avadh Saxena
We investigate a hybrid modeling framework in which a quantum annealer is used to simulate magnetic interactions in molecular qubit lattices inspired by experimentally realizable s…
Solitary waves in the complementary generalized ABS model
Avinash Khare, Fred Cooper, John F. Dawson +1
We obtain exact solutions of the nonlinear Dirac equation in 1+1 dimension of the form $ Ψ(x,t) =Φ(x) \rme^{-\rmi ωt}$ where the nonlinear interactions are a combination of vector-…
Connection Between the Exact Moving Solutions of the Negative Korteweg-de Vries (nKdV) Equation and the Negative Modified Korteweg-de Vries (nmKdV) Equation and the Static Solutions of 1+1 Dimensional Field Theory
Avinash Khare, Fred Cooper, Avadh Saxena
The negative order KdV (nKdV) and the modified KdV (nmKdV) equations have two different formulations based on different hierarchy operators. Both equations can be written in terms…
Solitary waves in a Two Parameter Family of Generalized Nonlinear Dirac Equations in Dimensions
Avinash Khare, Fred Cooper, John F. Dawson +1
We obtain exact solutions of the nonlinear Dirac equation in 1+1 dimension of the form where the nonlinear interactions are a combination of vector-vector…
Gravitational Waves beyond the Linear Approximation and Gravitational Wave Reflection
Victor Atanasov, Avadh Saxena
We derive a relativistic field equation for the trace of the metric perturbation beyond the weak field approximation to the Einstein field equations. The dynamics is governed by a…
Solitary waves in the coupled nonlinear massive Thirring as well as coupled Soler models with arbitrary nonlinearity
Avinash Khare, Fred Cooper, John F. Dawson +2
Motivated by the recent introduction of an integrable coupled massive Thirring model by Basu-Mallick et al, we introduce a new coupled Soler model. Further we generalize both the c…
Quantum matter and gravitation: photons in a waveguide
Victor Atanasov, Avadh Saxena
The conditions required by quantum matter to modify space-time geometry are explored within the framework of the general theory of relativity. The required characteristics for spac…
Mass Oscillations in Superconducting Junctions for Gravitational Wave Emission and Detection
Victor Atanasov, Avadh Saxena
We revisit the nonlinear superconducting junction dynamics in order to provide evidence that the time-dependent current density in the junction is related to an oscillating charge…
Time Operators and Time Crystals
K. Nakatsugawa, T. Fujii, A. Saxena +1
We investigate time operators in the context of quantum time crystals in ring systems. A generalized commutation relation called the generalized weak Weyl relation is used to deriv…
PT-Symmetric Dimer of Coupled Nonlinear Oscillators
J. Cuevas, P. G. Kevrekidis, A. Saxena +1
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.…