In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical problems. In particular, there is now a much deeper understanding of whyâ€¦ (More)

Quantum mechanical potentials satisfying the property of shape invariance are well known to be algebraically solvable. Using a scaling ansatz for the change of parameters, we obtain a large class ofâ€¦ (More)

We find new periodic solutions of the Kadomtsev-Petviashvili (KP) equation, the nonlinear SchrÃ¶dinger (NLS) equation, the Î»Ï†4 model, the sine-Gordon equation and the Boussinesq equation by makingâ€¦ (More)

Although eigenspectra of one dimensional shape invariant potentials with unbroken supersymmetry are easily obtained, this procedure is not applicable when the parameters in these potentialsâ€¦ (More)

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, the arguments ofâ€¦ (More)

Several nonlinear systems such as the Korteweg-de Vries (KdV) and modified KdV equations and lambda phi(4) theory possess periodic traveling wave solutions involving Jacobi elliptic functions. Weâ€¦ (More)

Motivated by the shape invariance condition in supersymmetric quantum mechanics, we develop an algebraic framework for shape invariant Hamiltonians with a general change of parameters. This approachâ€¦ (More)

Abstract. We derive a number of local identities involving Jacobi elliptic functions and use them to obtain several new results. First, we present an alternative, simpler derivation of the cyclicâ€¦ (More)