Lie Symmetries and Solitons in Nonlinear Systems with Spatially Inhomogeneous Nonlinearities

Juan Belmonte-Beitia, Víctor M. Pérez-García, Vadym Vekslerchik, and Pedro J. Torres
Phys. Rev. Lett. 98, 064102 – Published 5 February 2007

Abstract

Using Lie group theory and canonical transformations, we construct explicit solutions of nonlinear Schrödinger equations with spatially inhomogeneous nonlinearities. We present the general theory, use it to show that localized nonlinearities can support bound states with an arbitrary number solitons, and discuss other applications of interest to the field of nonlinear matter waves.

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  • Received 15 November 2006

DOI:https://doi.org/10.1103/PhysRevLett.98.064102

©2007 American Physical Society

Authors & Affiliations

Juan Belmonte-Beitia, Víctor M. Pérez-García, and Vadym Vekslerchik

  • Departamento de Matemáticas, Escuela Técnica Superior de Ingenieros Industriales, and Instituto de Matemática Aplicada a la Ciencia y la Ingeniería (IMACI), Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain

Pedro J. Torres

  • Departamento de Matemática Aplicada, Universidad de Granada, Campus de Fuentenueva s/n, 18071 Granada, Spain

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Issue

Vol. 98, Iss. 6 — 9 February 2007

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