in this paper, we consider non-linear ginsburg-pitaevski-gross equation with the rosen-morse and modifiedwoods-saxon potentials which is corresponding to the quantum vortices and has important applications in turbulence theory. we use the runge- kutta-fehlberg approximation method to solve the resulting non-linear equation.

A brief overviewof Forman’s discrete Morse theory is presented, from which analogues of the main results of classical Morse theory can be derived for discrete Morse functions, these being functions mapping the set of cells of a CW complex to the real numbers satisfying some combinatorial relations. The discrete analogue of the strong Morse inequality was proved by Forman for finite CW complexes...

A. In this paper we use Morse theory and the gradient flow of a Morse-Smale function to compute the linking number of a two-component link L in S 3 , by counting the signed number of gradient flow lines passing through each component of L. We will also use three Morse-Smale functions and their gradient flows, to compute Milnor's triple linking number of three-component links by counting ...

In [13] a homology theory –Morse-Conley-Floer homology– for isolated invariant sets of arbitrary flows on finite dimensional manifolds is developed. In this paper we investigate functoriality and duality of this homology theory. As a preliminary we investigate functoriality in Morse homology. Functoriality for Morse homology of closed manifolds is known [1, 2, 3, 8, 14], but the proofs use isom...

Let Γ be a finite d-valent graph and G an n-dimensional torus. An " action " of G on Γ is defined by a map which assigns to each oriented edge, e, of Γ, a one-dimensional representation of G (or, alternatively, a weight, αe, in the weight lattice of G. For the assignment, e → αe, to be a schematic description of a " G-action " , these weights have to satisfy certain compatibility conditions: th...

In this report, we discuss two papers that deal with computing Morse function on triangulated manifolds. Axen [1] gives an algorithm for computing Morse function on a triangulated manifold of arbitrary dimension but it not practical because of its space requirement. Hence, he describes an algorithm for computing critical points and their Morse indices for a 2-manifold. Edelsbrunner et al. [2] d...