In this article, we use the improved general mapping deformation method based on the generalized Jacobi elliptic functions expansion method with computerized symbolic computation to construct some new exact solutions for some nonlinear partial differential equations via the cubic nonlinear Klein Gordon equation and the modified Kawahara equation. As a result, new generalized Jacobi elliptic fun...

A unified basic frame of rational expansion methods is presented, which leads to closed-form solutions of nonlinear evolution equations (NLEEs). The new unified algorithms are given to find exact rational formal polynomial solutions of NLEEs in terms of Jacobi elliptic functions, solutions of the Riccati equation and solutions of the generalized Riccati equation. They can be implemented in symb...

We consider space and time dependent fuzzy spheres S 2p arising in D1 − D(2p + 1) intersections in IIB string theory and collapsing D(2p)-branes in IIA string theory. In the case of S 2 , where the periodic space and time-dependent solutions can be described by Jacobi elliptic functions, there is a duality of the form r to 1 r which relates the space and time dependent solutions. This duality i...

The theory of the classical Jacobi forms on H × C has been studied extensively by Eichler and Zagier[?]. Ziegler[?] developed a more general approach of Jacobi forms of higher degree. In [?] and [?], Gritsenko and Krieg studied Jacobi forms on H × Cn and showed that these kinds of Jacobi forms naturally arise in the Jacobi Fourier expansions of all kinds of automorphic forms in several variable...

Certain “index shifting operators” for local and global representations of the Jacobi group are introduced. They turn out to be the representation theoretic analogues of the Hecke operators Ud and Vd on classical Jacobi forms, which underlie the theory of Jacobi oldand new-forms. Further analogues of these operators on spaces of classical elliptic cusp forms are also investigated. In view of th...

We generalize Warnaar's elliptic extension of a Macdonald multi-parameter summation formula to Riemann surfaces of arbitrary genus. We start by a brief outline of the general theory of hypergeometric type series built from Jacobi theta functions [12, 13] (its extension to integrals [15] is not touched at all). Within this approach univariate elliptic hypergeometric series are defined as the ser...

In this article, we examine the Perturbed Gerdjikov-Ivanov equation by using Jacobi elliptic function expansion method. This results in obtaining distinct solutions including dark, bright, singular solitons, periodic waves, and solutions. The 2- 3-dimensional graphs of reported are presented. may be useful explaining physical features studied equation.

This study presents utilization of Jacobi elliptic function expansion method to obtain the di¤erent types solutions 3+1dimensional Boussinesq equation with dual dispersion. By using this hyperbolic and trigonometric functionsolutions are also obtained. The resulting outcomes verify that preferred is valid reliable for analytical technique an extensive application nonlinear phenomena.

We consider space and time dependent fuzzy spheres S 2p arising in D1 − D(2p + 1) intersections in IIB string theory and collapsing D(2p)-branes in IIA string theory. In the case of S 2 , where the periodic space and time-dependent solutions can be described by Jacobi elliptic functions, there is a duality of the form r to 1 r which relates the space and time dependent solutions. This duality i...

This article is devoted to an investigation of a reality condition of a hyperelliptic loop soliton of higher genus. In the investigation, we have a natural extension of Jacobi am-function for an elliptic curves to that for a hyperelliptic curve. We also compute winding numbers of loop solitons.