2.7k citations · 6.2k across the 194 of their papers we have counts for
25 papers · 1 filter
Solutions of (1+1)-dimensional Dirac equation associated with exceptional orthogonal polynomials and the parametric symmetry
Suman Banerjee, Rajesh Kumar Yadav, Avinash Khare +2
We consider -dimensional Dirac equation with rationally extended scalar potentials corresponding to the radial oscillator, the trigonometric Scarf and the hyperbolic Poschl-Te…
Rationally extended many-body truncated Calogero-Sutherland model
Rajesh Kumar Yadav, Avinash Khare, Nisha Kumari +1
We construct a rational extension of the truncated Calogero-Sutherland model by Pittman et al. The exact solution of this rationally extended model is obtained analytically and it…
A short note on "Group theoretic approach to rationally extended shape invariant potentials" [Annals of Physics 359, 46 (2015)]
Arturo Ramos, Bijan Bagchi, Avinash Khare +3
It is proved the equivalence of the compatibility condition of [A. Ramos, J. Phys. A 44 (2011) 342001, Phys. Lett. A 376 (2012) 3499] with a condition found in [Yadav et al., Ann.…
Superposition of Elliptic Functions as Solutions For a Large Number of Nonlinear Equations
Avinash Khare, Avadh Saxena
For a large number of nonlinear equations, both discrete and continuum, we demonstrate a kind of linear superposition. We show that whenever a nonlinear equation admits solutions i…
Successive phase transitions and kink solutions in , , and field theories
Avinash Khare, Ivan C. Christov, Avadh Saxena
We obtain exact solutions for kinks in , and field theories with degenerate minima, which can describe a second-order phase transition followed by a first-…
The Scattering amplitude for Newly found exactly solvable Potential
Rajesh Kumar Yadav, Avinash Khare, Bhabani Prasad Mandal
The scattering amplitude for the recently discovered exactly solvable shape invariant potential, which is isospectral to the generalized Pöschl-Taylor potential, is calculated expl…
A proof of the nodal structure of the wave functions of supersymmetric partner potentials
S. Sree Ranjani, A. K. Kapoor, A. Khare +1
Quantum Hamilton-Jacobi formalism is used to give a proof for Gozzi's criterion that for eigenstates of the supersymmetric partners, corresponding to same energy, the difference in…
New QES Hermitian as well as non-Hermitian PT invariant Potentials
Avinash Khare, Bhabani Prasad Mandal
We start with quasi-exactly solvable (QES) Hermitian (and hence real) as well as complex PT-invariant, double sinh-Gordon potential and show that even after adding perturbation ter…
Solutions of Several Coupled Discrete Models in terms of Lame Polynomials of Arbitrary Order
Avinash Khare, Avadh Saxena, Apoorva Khare
Coupled discrete models abound in several areas of physics. Here we provide an extensive set of exact quasiperiodic solutions of a number of coupled discrete models in terms of Lam…
Exceptional orthogonal polynomials, QHJ formalism and SWKB quantization condition
S. Sree Ranjani, P. K. Panigrahi, A. Khare +2
We study the quantum Hamilton-Jacobi (QHJ) equation of the recently obtained exactly solvable models, related to the newly discovered exceptional polynomials and show that the QHJ…
Solitary wave in the Nonlinear Dirac Equation with arbitrary nonlinearity
Fred Cooper, Avinash Khare, Bogdan Mihaila +1
We consider the nonlinear Dirac equations (NLDE's) in 1+1 dimension with scalar-scalar self interaction , as well as a vector-vector self intera…
Compactons in PT-symmetric generalized Korteweg-de Vries Equations
Carl M. Bender, Fred Cooper, Avinash Khare +2
In an earlier paper Cooper, Shepard, and Sodano introduced a generalized KdV equation that can exhibit the kinds of compacton solitary waves that were first seen in equations studi…
Higher Order Periodic Solutions of Coupled phi4 Models
Avinash Khare, Avadh Saxena
We obtain several higher order exact periodic solutions of (i) a coupled symmetric phi4 model in an external field, (ii) an asymmetric coupled phi4 model, (iii) an asymmetric-symme…
Quasi-Periodic Solutions of Heun's Equation
Avinash Khare, Uday Sukhatme
By exploiting a recently developed connection between Heun's differential equation and the generalized associated Lamé equation, we not only recover the well known periodic solutio…
PT-Invariant Periodic Potentials with a Finite Number of Band Gaps
Avinash Khare, Uday Sukhatme
We obtain the band edge eigenstates and the mid-band states for the complex, PT-invariant generalized associated Lamé potentials $V^{PT}(x)=-a(a+1)m \sn^2(y,m)-b(b+1)m {\sn^2 (y+K(…
Supersymmetry in Quantum Mechanics
Avinash Khare
An elementary introduction is given to the subject of Supersymmetry in Quantum Mechanics. We demonstrate with explicit examples that given a solvable problem in quantum mechanics w…
Cyclic Identities Involving Ratios of Jacobi Theta Functions
Avinash Khare, Arul Lakshminarayan, Uday Sukhatme
Identities involving cyclic sums of terms composed from Jacobi elliptic functions evaluated at equally shifted points were recently found. The purpose of this paper is to re-ex…
Generalized Landen Transformation Formulas for Jacobi Elliptic Functions
Avinash Khare, Uday Sukhatme
Landen transformation formulas, which connect Jacobi elliptic functions with different modulus parameters, were first obtained over two hundred years ago by changing integration va…
Local Identities Involving Jacobi Elliptic Functions
Avinash Khare, Arul Lakshminarayan, Uday Sukhatme
We derive a number of local identities of arbitrary rank involving Jacobi elliptic functions and use them to obtain several new results. First, we present an alternative, simpler d…
Relating Linearly Superposed Periodic Solutions of Nonlinear Equations to One Soliton Solutions
W. Reinhardt, A. Khare, U. Sukhatme
Using new generalized Landen transformations, we prove that the solutions of the KdV and other nonlinear equations obtained recently by using a kind of superposition principle for…
Cyclic Identities Involving Jacobi Elliptic Functions. II
Avinash Khare, Arul Lakshminarayan, Uday Sukhatme
Identities involving cyclic sums of terms composed from Jacobi elliptic functions evaluated at equally shifted points on the real axis were recently found. These identities pla…
A Generalization of Landen's Quadratic Transformation Formulas for Jacobi Elliptic Functions
Avinash Khare, Uday Sukhatme
Landen formulas, which connect Jacobi elliptic functions with different modulus parameters, were first obtained over two hundred years ago by making a suitable quadratic transforma…
Cyclic Identities Involving Jacobi Elliptic Functions
Avinash Khare, Uday Sukhatme
We state and discuss numerous mathematical identities involving Jacobi elliptic functions sn(x,m), cn(x,m), dn(x,m), where m is the elliptic modulus parameter. In all identities, t…
Linear Superposition in Nonlinear Equations
Avinash Khare, Uday Sukhatme
Even though the KdV and modified KdV equations are nonlinear, we show that suitable linear combinations of known periodic solutions involving Jacobi elliptic functions yield a larg…