The elliptic genus (EG) of a compact complex manifold was introduced as a holomorphic Euler characteristic of some formal power series with vector bundle coefficients. EG is an automorphic form in two variables only if the manifold is a Calabi–Yau manifold. In physics such a function appears as the partition function of N = 2 superconformal field theories. In these notes we define the modified ...

This paper provides new results about efficient arithmetic on (extended) Jacobiquartic form elliptic curves y = dx + 2ax + 1. Recent works have shown thatarithmetic on an elliptic curve in Jacobi quartic form can be performed solidly fasterthan the corresponding operations in Weierstrass form. These proposals use up to 7coordinates to represent a single point. However, fast scal...

In this paper we find division polynomials for Huff curves, Jacobi quartics, and Jacobi intersections. These curves are alternate models for elliptic curves to the more common Weierstrass curve. Division polynomials for Weierstrass curves are well known, and the division polynomials we find are analogues for these alternate models. Using the division polynomials, we show recursive formulas for ...

In this paper, by using a direct method based on the Jacobi elliptic functions, exact solutions of space-time fractional symmetric regularized long wave (SRLW) equation have been obtained. The function nonlinear ordinary differential (auxiliary) $\left({dF}/{d \xi}\right) ^{2} = PF^{4} (\xi)+QF^{2} (\xi) + R$ also examined. Besides, found in general form including rational, trigonometric and hy...

We prove that the effective nonlinearities (ergodic constants) obtained in the stochastic homogenization of Hamilton-Jacobi, “viscous” Hamilton-Jacobi and nonlinear uniformly elliptic pde are approximated by the analogous quantities of appropriate “periodizations” of the equations. We also obtain an error estimate, when there is a rate of convergence for the stochastic homogenization.

From any given Frobenius manifold one may construct a so-called ‘dual’ structure which, while not satisfying the full axioms of a Frobenius manifold, shares many of its essential features, such as the existence of a prepotential satisfying the WDVV equations of associativity. Jacobi group orbit spaces naturally carry the structures of a Frobenius manifold and hence there exists a dual prepotent...

A double sub-equation method is presented for constructing complexiton solutions of nonlinear partial differential equations (PDEs). The main idea of the method is to take full advantage of two solvable ordinary differential equations with different independent variables. With the aid of Maple, one can obtain both complexiton solutions, combining elementary functions and the Jacobi elliptic fun...

Our paper studies the optical solitons for Kundu–Eckhaus (KE) equation with quintic nonlinearity and Raman effect. By applying improved modified extended tanh-function method, many soliton solutions can be obtained such as bright solutions, dark singular solution. In addition, we obtain various types of namely, periodic exponential rational Jacobi elliptic Weierstrass doubly solutions. Moreover...