Publication Date
2015
Abstract
In the present paper we consider an optical system with a χ (2)-type nonlinearity and unspecified PT -symmetric potential functions. Considering this as an inverse problem and positing a family of exact solutions in terms of cnoidal functions, we solve for the resulting potential functions in a way that ensures the potentials obey the requirements of PT -symmetry. We then focus on case examples of soliton and periodic solutions for which we present a stability analysis as a function of their amplitude parameters. Finally, we numerically explore the nonlinear dynamics of the associated waveforms to identify the outcome of the relevant dynamical instabilities of localized and extended states.
Pages
16 pp.
Recommended Citation
Truong Vu, Y. N.; D'Ambroise, J.; Abdullaev, F. Kh.; and Kevrekidis, P. G., "Some Case Example Exact Solutions for Quadratically Nonlinear Optical Media with PT-Symmetric Potentials" (2015). Mathematics and Statistics Department Faculty Publication Series. 1220.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/1220
Comments
Arxiv preprint uploaded.