Jacobian elliptic function

Jacobian elliptic function

[jə′kō·bē·ən ə¦lip·tik ′fəŋk·shən]
(mathematics)
For m a real number between 0 and 1, and u a real number, let φ be that number such that the 12 Jacobian elliptic functions of u with parameter m are sn (u | m) = sin φ, cn (u | m) = cos φ, dn (u | m) = (1-m sin2φ)1/2, the reciprocals of these three functions, and the quotients of any two of them.
References in periodicals archive ?
We have the hyperbolic function solutions, trigonometric function solutions, and the Jacobian elliptic function solutions.
In this section, corresponding to all phase orbits given by Section 2, through qualitative analysis and the Jacobian elliptic functions [12], we discuss the exact travelling wave solutions of (3).
occur in the theory of Jacobian theta functions and their applications to Jacobian elliptic functions.
Here the modulus k of Jacobian elliptic functions is determined uniquely as [k.
Here, dn(z; [beta]) and cn(z; [beta]) are the Jacobian elliptic functions for z = [alpha](x - [x.
We choose two solutions in the form of a combination of Jacobian Elliptic functions (with an appropriate phase factor).
Reduction of the doubly periodic Weierstrass function p to a set of single periodic Jacobian elliptic functions is based on the following relationship between p and cn, sn with modulus M: