Abstract
A “transparent point” is a particular value of a governing parameter in a nontranslationally invariant system that makes the system “almost” translationally invariant. This concept was introduced recently in the context of the discrete nonlinear Schrodinger (DNLS) equation with saturable nonlinearity — it was discovered that a tuning of the lattice spacing parameter h in this model affects the soliton mobility. In this paper, we study the DNLS equation with competing cubic–quintic nonlinearity that also admits the transparent points with respect to the lattice spacing parameter h. We give a geometrical interpretation of the transparent points in terms of dynamical system theory and present a simple asymptotical formula for them at h → 0. Although the derivation of this formula is heuristic and nonrigorous, it gives the values of transparent points with remarkable accuracy even for quite large values of h.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
