Eur. Phys. J. Plus (2019) 134: 16
https://doi.org/10.1140/epjp/i2019-12456-x

Regular Article

Nonlinear scattering and its transfer matrix formulation in one dimension

Departments of Mathematics and Physics, Koç University, 34450 Sarıyer, Istanbul, Turkey

^* e-mail: amostafazadeh@ku.edu.tr

Received: 23 October 2018
Accepted: 7 December 2018
Published online: 11 January 2019

Abstract

We present a systematic formulation of the scattering theory for nonlinear interactions in one dimension and develop a nonlinear generalization of the transfer matrix that has a composition property similar to that of its linear analog. We offer alternative characterizations of spectral singularities, unidirectional reflectionlessness and invisibility, and nonreciprocal transmission for nonlinear scattering systems, and examine the application of our general results in addressing the scattering problem for nonlinear single- and double--function potentials.