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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…
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…
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…
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-…
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…
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…
Exact trapped -soliton solutions of the nonlinear Schrödinger equation using the inverse problem method
Fred Cooper, Avinash Khare, John F. Dawson +2
In this work, we show the application of the ``inverse problem'' method to construct exact trapped soliton-like solutions of the nonlinear Schrödinger or Gross-Pitaevskii equat…
Higher order complex cubic quintic Ginzburg Landau equation : Chirped solitary waves
Naresh Saha, Baranana Roy, Avinash Khare
Propagation characteristics of the chirped dissipative solitary waves are investigated within the framework of higher order complex cubic quintic Ginzburg Landau equation. Potentia…
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…
How close Are Integrable and Non-integrable Models: A Parametric Case Study Based on the Salerno Model
Thudiyangal Mithun, Aleksandra Maluckov, Ana Mančić +2
In the present work we revisit the Salerno model as a prototypical system that interpolates between a well-known integrable system (the Ablowitz-Ladik lattice) and an experimentall…
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…
Dipole and quadrupole nonparaxial solitary waves
Naresh Saha, Barnana Roy, Avinash Khare
The cubic nonlinear Helmholtz equation with third and fourth order dispersion and non-Kerr nonlinearity like the self steepening and the self frequency shift is considered. This mo…
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.…
Chirped Elliptic Waves: Coupled Helmholtz Equations
Naresh Saha, Barnana Roy, Avinash Khare
Exact chirped elliptic wave solutions are obtained within the framework of coupled cubic nonlinear Helmholtz equations in the presence of non-Kerr nonlinearity like self steepening…
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…
Coupled Helmholtz Equations : Chirped Solitary Waves
Naresh Saha, Barnana Roy, Avinash Khare
We investigate the existence and stability properties of the chirped gray and anti-dark solitary waves within the framework of coupled cubic nonlinear Helmholtz equation in the pre…
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…