We show that the formalism of supersymmetric quantum mechanics applied to the solvable elliptic function potentials V (x) = mj(j + 1)sn(x,m) produces new exactly solvable onedimensional periodic potentials. In a recent paper, Dunne and Feinberg [1] have systematically discussed various aspects of supersymmetric quantum mechanics (SUSYQM) as applied to periodic potentials. In particular, they de...

In this paper, with the aid of symbolic computation we improve the extended F-expansion method described in Chaos, Solitons and Fractals 22, 111 (2004) to solve the (2 +1)-dimensional Korteweg de Vries equation. Using this method, we derive many exact non-travelling wave solutions. These are more general than the previous solutions derived with the extended F-expansion method. They include the ...

In this paper we make use of the the sn-ns method to obtain new exact solutions to so called repulsive or de-focusing nonlinear Schrödinger equation. These solutions are given in terms of Jacobi elliptic functions sn and ns.

We give explicit formulas for the number of distinct elliptic curves over a finite field, up to isomorphism, in the families of Legendre, Jacobi, Hessian and generalized Hessian curves.

‎in this paper‎, ‎we obtain exact solutions involving parameters of some nonlinear pdes in mathmatical physics; namely the one-‎dimensional modified complex ginzburg-landau equation by using the $ (g^{'}/g) $ expansion method‎, homogeneous balance method, extended f-expansion method‎. ‎by ‎using homogeneous balance principle and the extended f-expansion, more periodic wave solutions expres...

We have considered flat Friedmann-Robertson-Walker (FRW) model of the universe and reviewed modified Chaplygin gas as fluid source. Associated with scalar field model, we determined Hubble parameter a generating function in terms field. Instead hyperbolic function, taken Jacobi elliptic Abel obtained Chaplygin-Jacobi (MCJG) Chaplygin-Abel (MCAG) equation states, respectively. Next, assumed that...

Invalid curve attacks are a well-known class of attacks against implementations of elliptic curve cryptosystems, in which an adversary tricks the cryptographic device into carrying out scalar multiplication not on the expected secure curve, but on some other, weaker elliptic curve of his choosing. In their original form, however, these attacks only affect elliptic curve implementations using ad...

In this article we identify several beautiful properties of Jacobi sums that become evident when these numbers are organized as a matrix and studied via the tools of linear algebra. In the process we reconsider a convention employed in computing Jacobi sum values by illustrating how these properties become less elegant or disappear entirely when the standard definition for Jacobi sums is utiliz...

This paper establishes relationships between elliptic functions and Riordan arrays leading to new classes of which here are called arrays. In particular, the case of...