2 citations · 5 across the 4 of their papers we have counts for
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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…
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…
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…
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…