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On Some Classes of mKdV Periodic Solutions
P. G. Kevrekidis, Avinash Khare, A. Saxena +1
We obtain exact periodic solutions of the positive and negative modified Kortweg-de Vries (mKdV) equations. We examine the dynamical stability of these solitary wave lattices throu…
Solitary Wave Interactions In Dispersive Equations Using Manton's Approach
P. G. Kevrekidis, Avinash Khare, A. Saxena
We generalize the approach first proposed by Manton [Nuc. Phys. B {\bf 150}, 397 (1979)] to compute solitary wave interactions in translationally invariant, dispersive equations th…
Exact Solutions of the Saturable Discrete Nonlinear Schrodinger Equation
Avinash Khare, K. O. Rasmussen, M. R. Samuelsen +1
Exact solutions to a nonlinear Schr{ö}dinger lattice with a saturable nonlinearity are reported. For finite lattices we find two different standing-wave-like solutions, and for an…
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…
Supersymmetric Quantum Mechanics on Non-Commutative Plane
E. Harikumar, V. Sunil Kumar, Avinash Khare
We study the Pauli equation on non-commutative plane. It is shown that the Supersymmetry algebra holds to all orders in the non-commutative parameter in case the gyro-magnetic…