The plate perimeter is defined by a super elliptic function with a power defining the shape ranging from an ellipse to a rectangle.
The pressure drop in hollow fibers is formulated by an elliptic integral function, and the effectiveness factor of the transmembrane pressure is proposed to characterize the effect.
Lü [31] solved Eq. (1) by a general Jacobi elliptic function expansion method, and obtained Jacobi elliptic function solutions.
It is a combination of a Jacobi elliptic function and a trigonometric function.
Our results show that the complex method is simpler than the other methods, and there exist some rational solutions w r, 2 ( z ) and simply periodic solutions w s, 2 ( z ) such that they are not only new but also not degenerated successively by the elliptic function solutions.
Our results show that the complex method is simpler than other methods, and there exist some rational solutions w r, 2 ( z ) and simply periodic solutions w s, 2 ( z ) which are not only new but also not degenerated successively by the elliptic function solutions.
Our results show that all rational and simply periodic exact traveling wave solutions of the combined KdV-mKdV equation are solitary wave solutions, the complex method is simpler than other methods, and there exist some rational solutions w r, 2 ( z ) and simply periodic solutions w s, 2 ( z ) such that they are not only new but also not degenerated successively by the elliptic function solutions.
The loading function is derived from the free oscillation response whose time course follows a Jacobi elliptic function.
Our first lemma shows the existence of a uniformly elliptic function under conditions A1, A2 and A1*.
2, we investigate it by making use of an elliptic modular function as well as the punctured unit disk model.
