Statistical mechanics of a discrete Schrödinger equation with saturable nonlinearity

• Published in: Physical review. E, Statistical, nonlinear, and soft matter physics Vol. 87; no. 4; p. 044901
• Main Authors: Samuelsen, Mogens R, Khare, Avinash, Saxena, Avadh, Rasmussen, Kim Ø
• Format: Journal Article
• Language: English
• Published: United States American Physical Society 17-04-2013
• ISSN: 1539-3755; 1550-2376
• DOI: 10.1103/PhysRevE.87.044901

We study the statistical mechanics of the one-dimensional discrete nonlinear Schrödinger (DNLS) equation with saturable nonlinearity. Our study represents an extension of earlier work [Phys. Rev. Lett. 84, 3740 (2000)] regarding the statistical mechanics of the one-dimensional DNLS equation with a cubic nonlinearity. As in this earlier study, we identify the spontaneous creation of localized excitations with a discontinuity in the partition function. The fact that this phenomenon is retained in the saturable DNLS is nontrivial, since in contrast to the cubic DNLS whose nonlinear character is enhanced as the excitation amplitude increases, the saturable DNLS, in fact, becomes increasingly linear as the excitation amplitude increases. We explore the nonlinear dynamics of this phenomenon by direct numerical simulations.