Z. Naturforsch. **68a,** 255 – 260
(2013)

doi:10.5560/ZNA.2012-0108

Integral Methods to Solve the Variable Coefficient Nonlinear Schrödinger Equation

Rehab
Mahmoud El-Shiekh and
Abdul-Ghani
Al-Nowehy

Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Hiliopolis, Cairo, Egypt

Received July 31, 2012 / revised September 25, 2012 / published online January 23, 2013

In this paper, we use two different integral techniques, the first integral and the direct integral method, to study the variable coefficient nonlinear Schrödinger (NLS) equation arising in arterial mechanics. The application of the first integral method yielded periodic and solitary wave solutions. Using the direct integration lead to solitary wave solution and Jacobi elliptic function solutions.

*Key words:* NLS Equation with Variable Coefficient; First Integral Method; Direct Integral Method; Periodic, Solitary and Jacobi Elliptic Function Solutions.