We take into account the (2 + 1)-dimensional stochastic Kadomtsev–Petviashvili equation with beta-derivative (SKPE-BD) in this paper. To develop new hyperbolic, trigonometric, elliptic, and rational solutions, Riccati Jacobi elliptic function methods are employed. Because KP is required for explaining development of quasi-one-dimensional shallow-water waves, solutions obtained can be used to in...

The second elliptic equation method is a more general form of Jacobi function expansion method, which can obtain kinds solutions nonlinear evolution equation. In this paper, the used to solve Kdv-Burgers-Kuramoto (Benny) with variable coefficients, and its extremely rich solution properties are elucidated, among biperiodic solutions, solitary wave trigonometric periodic analyzed graphically.

The use of elliptic curve cryptosystems on embedded systems has been becoming widespread for some years. Therefore the resistance of such cryptosystems to side-channel attacks is becoming crucial. Several techniques have recently been developed. One of these consists of finding a representation of the elliptic curve such that formulae for doubling and addition are the same. Until now, the best ...

This study consider Gerdjikov-Ivanov equation where the perturbation terms appear with full non-linearity. The Jacobi elliptic function ansatz method is implemented to obtain exact solutions of this that models pulse dynamics in optical fibers. It retrieved some bright, dark and singular solitons profile limiting cases functions. constraint conditions depending on parameters for existence are a...

First we give a compact treatment of the Jacobi polynomials on a simplex in IR which exploits and emphasizes the symmetries that exist. This includes the various ways that they can be defined: via orthogonality conditions, as a hypergeometric series, as eigenfunctions of an elliptic pde, as eigenfunctions of a positive linear operator, and through conditions on the Bernstein–Bézier form. We the...

We modified the rational Jacobi elliptic functions method to construct some new exact solutions for nonlinear differential difference equations in mathematical physics via the lattice equation, the discrete nonlinear Schrodinger equation with a saturable nonlinearity, the discrete nonlinear Klein-Gordon equation, and the quintic discrete nonlinear Schrodinger equation. Some new types of the Jac...

In the sense of a conformable fractional operator, we consider generalized fractional–stochastic nonlinear wave equation (GFSNWE). This may be used to depict several physical phenomena occurring in liquid containing gas bubbles. The analytical solutions GFSNWE are obtained by using F-expansion and Jacobi elliptic function methods with Riccati equation. Due presence noise derivative, some that w...

Every elliptic curve of even order over a finite field of characteristic > 3 is birationally equivalent to a curve in the Jacobi quartic form. In this paper, new explicit formulae for group operations on a Jacobi quartic curve are presented. The algorithm for doubling uses only 1M +6S, for the mixed-addition uses only 8M + 2S and the unified addition formula only 9M + 2S to the best case. For e...

This paper is on efficient implementation techniques of Elliptic Curve Cryptography. We improve group operation timings for Hessian and Jacobi-intersection forms of elliptic curves. In this study, traditional coordinates of these forms are modified to speed up the addition operations. For the completeness of our study, we also recall the modified Jacobiquartic coordinates which benefits from si...

In this paper, based on the close relationship between the Weierstrass elliptic function ℘(ξ; g2, g3)(g2, g3, invariants) and nonlinear ordinary differential equation, a Weierstrass elliptic function expansion method is developed in terms of the Weierstrass elliptic function instead of many Jacobi elliptic functions. The mechanism is constructive and can be carried out in computer with the aid ...