Threshold of damped critical non-linear Schrödinger equation with fourth-order dispersion

Abstract

This article is concerned with a damped critical non-linear Schrödinger equation with fourth-order dispersion which models propagation of fibre arrays in non-linear Kerr media. We analyse the effect of the damping force on the solution for the system and prove that there exists a threshold value of the damping parameter for global existence and blowup of the system. Furthermore, we estimate the threshold value.

Keywords:

• threshold
• damped
• critical
• non-linear Schrödinger equation
• fourth-order dispersion

2000 MR Subject Classifications:

• 78A60
• 35Q55

Acknowledgement

This work is supported by the National Science Foundation of China (Grant no. 10771151 and no. 10726033), the Scientific Research Found of Sichuan Provincial Education Department (Grant no. 2006A063) and the Scientific Research Found of Science and Technology Bureau of Sichuan Province (Grant no. 07JY029-012).