Communications in Physics, Vol. 20, No. 1 (2010), pp. 31-36 DYNAMICS OF COLLAPSE OF OPTICAL PULSES IN KERR MEDIUM PLACED IN A HARMONIC POTENTIAL CAO LONG VAN Institute of Physics, University of Zielona G´ ora, Podg´ orna 50, 65-246 Zielona G´ ora, Poland DINH XUAN KHOA Vinh University, Nghe An, Vietnam NGUYEN VIET HUNG Soltan Institute for Nuclear Studies, Ho˙ za 69, 00-681 Warsaw, Poland M. TRIPPENBACH Department of physics, Warsaw University, Ho˙ za 69, 00-681 Warsaw, Poland Abstract. We consider the propagation of optical pulses in Kerr medium placed in a harmonic potential for 2D case in framework of Variational Approximation (VA). We will use two types of trial function: gaussian and hyperbolic secant. We will show that for the values of the nonlinearity parameter bigger than a certain critical value the pulses will collapse. This corresponds to the physical situation when the self-focusing dominates over the dispersion and diffraction. We will confirm this by numerical calculations which are in excellent agreement with the VA predictions. I. INTRODUCTION Consideration of the self-focusing effect in nonlinear optics is interesting both the- oretically and practically. Theoretically, because sometimes we can see dramatic concur- rence between different nonlinear effects of the pulse propagation in the nonlinear medium. When the self-focusing effect dominates over the other effects as the dispersion, diffraction etc. the amplitude of the optical pulse (soliton) increases drastically. In a critical point the pulse completely collapses. In practice this phenomenon is very dangerous because it usually destroys the optical material. By analogy between nonlinear optics in a Kerr medium and the Bose-Einstein condensate (BEC) system [1], all results of this considera- tion can be transferred in to the BEC systems. For some values of the nonlinear coupling constant we can have the collapse and the explosion of the BEC [2]. The collapse of self-focusing waves described by the nonlinear Schr¨ odinger equation (NLSE) in nonlinear optics and plasma turbulence is reviewed in [5]. In this paper using the variational ap- proximation (VA) we will predict the critical point in which the optical pulse collapses. In the VA the choice of the trial functions is essential. There are two perspective ones for this situation, namely the Gaussian Ansatz and the Secant Ansatz. Here we have done variational calculations for two types of such trial functions. By confirming numerically our analytical predictions through the use of time imaginary method [3] we have concluded that the secant trial function is more proper. This fact is quite understandable because