A new numerical scheme for computing self-localized states - or solitons - of nonlinear waveguides is proposed. The idea behind the method is to transform the underlying equation governing the soliton, such as a nonlinear Schrödinger-type equation, into Fourier space and determine a nonlinear nonlocal integral equation coupled to an algebraic equation. The coupling prevents the numerical scheme from diverging. The nonlinear guided mode is then determined from a convergent fixed point iteration scheme. This spectral renormalization method can find wide applications in nonlinear optics and related fields such as Bose-Einstein condensation and fluid mechanics.
© 2005 Optical Society of America
Mark J. Ablowitz and Ziad H. Musslimani, "Spectral renormalization method for computing self-localized solutions to nonlinear systems," Opt. Lett. 30, 2140-2142 (2005)