Results 1 to 10 of about 29,678 (237)

Local Identities Involving Jacobi Elliptic Functions [PDF]

Pramana, 2003
We derive a number of local identities of arbitrary rank involving Jacobi elliptic functions and use them to obtain several new results. First, we present an alternative, simpler derivation of the cyclic identities discovered by us recently, along with ...
A Khare, A Khare, Arul Lakshminarayan, Avinash Khare, I S Gradshteyn, M Abramowitz, P F Byrd, Uday Sukhatme   +7 more
core   +7 more sources

Cyclic Identities Involving Jacobi Elliptic Functions [PDF]

Journal of Mathematical Physics, 2002
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 of the Jacobi functions are separated by either 2K(m)/p or 4K(
Avinash Khare, Khare A., Khare A., Uday Sukhatme   +3 more
core   +4 more sources

Cyclic identities for Jacobi elliptic and related functions [PDF]

Journal of Mathematical Physics, 2003
Identities involving cyclic sums of terms composed from Jacobi elliptic functions evaluated at p equally shifted points on the real axis were recently found. These identities played a crucial role in discovering linear superposition solutions of a large number of important nonlinear equations. We derive four master identities, from which the identities
Khare, Avinash, Lakshminarayan, Arul, Sukhatme, Uday   +2 more
openaire   +4 more sources

New Exact Jacobi Elliptic Function Solutions for the Coupled Schrödinger-Boussinesq Equations [PDF]

Journal of Applied Mathematics, 2013
A general algebraic method based on the generalized Jacobi elliptic functions expansion method, the improved general mapping deformation method, and the extended auxiliary function method with computerized symbolic computation is proposed to construct ...
Baojian Hong, Dianchen Lu
doaj   +2 more sources

Construction of exotical soliton-like for a fractional nonlinear electrical circuit equation using differential-difference Jacobi elliptic functions sub-equation method

Results in Physics, 2022
The deal of this paper is to use the differential-difference Jacobi elliptic functions sub-equation method for constructing exact solutions of nonlinear electrical circuit including intrinsic fractional-order in the sense of Riemann–Liouville derivatives.
Emmanuel Fendzi-Donfack, Dipankar Kumar, Eric Tala-Tebue, Laurent Nana, Jean Pierre Nguenang, Aurélien Kenfack-Jiotsa   +5 more
doaj   +3 more sources

Periodic structures of solitons and shock wave solutions in the fractional nonlinear Shynaray-IIA equation via a generalized analytical method [PDF]

Scientific Reports
In this research, we utilized the Jacobi elliptic function expansion method to study the truncated M-fractional nonlinear Shynaray-IIA (S-IIA) equation with computational simulations. With the use of a truncated M-fractional derivative, the nonlinear (1 +
Mujahid Iqbal, Muhammad Ishfaq Khan, Huda Daefallh Alrashdi, Reem Algethamie, Faizah A. H. Alomari, Abeer Aljohani, Nazar Mohammad, Salma Aljawi   +7 more
doaj   +2 more sources

Jacobi Elliptic Cliffordian Functions [PDF]

Complex Variables and Elliptic Equations, 2002
The well-known Jacobi elliptic functions sn(z)$, $cn(z), dn(z) are defined in higher dimensional spaces by the following method. Consider the Clifford algebra of the antieuclidean vector space of dimension 2m+1. Let x be the identity mapping on the space of scalars + vectors.
Laville, Guy, Ramadanoff, Ivan
exaly   +3 more sources

New Jacobi Elliptic Function Solutions for the Zakharov Equations [PDF]

Journal of Applied Mathematics, 2012
A generalized (G′/G)‐expansion method is proposed to seek the exact solutions of nonlinear evolution equations. Being concise and straightforward, this method is applied to the Zakharov equations. As a result, some new Jacobi elliptic function solutions of the Zakharov equations are obtained. This method can also be applied to other nonlinear evolution
Yun-Mei Zhao
openaire   +6 more sources

A Nonlinear Differential Equation Related to the Jacobi Elliptic Functions [PDF]

International Journal of Differential Equations, 2012
A nonlinear differential equation for the polar angle of a point of an ellipse is derived. The solution of this differential equation can be expressed in terms of the Jacobi elliptic function dn(u,k).
Kim Johannessen
doaj   +5 more sources

Jacobi Elliptic Functions and the Complete Solution to the Bead on the Hoop Problem [PDF]

, 2012
Jacobi elliptic functions are flexible functions that appear in a variety of problems in physics and engineering. We introduce and describe important features of these functions and present a physical example from classical mechanics where they appear: a
Baker, Thomas E., Bill, Andreas
core   +2 more sources