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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…
Complex Optical Potentials and Pseudo-Hermitian Hamiltonians
Ram Narayan Deb, Avinash Khare, Binayak Dutta Roy
Recently some authors have broadened the scope of canonical quantum mechanics by replacing the conventional Hermiticity condition on the Hamiltonian by a weaker requirement through…
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…
Periodic Solutions of Nonlinear Equations Obtained by Linear Superposition
Fred Cooper, Avinash Khare, Uday Sukhatme
We show that a type of linear superposition principle works for several nonlinear differential equations. Using this approach, we find periodic solutions of the Kadomtsev-Petviashv…
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…