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Phys Rev Lett. 2008 Apr 25;100(16):164102. Epub 2008 Apr 25.

Localized nonlinear waves in systems with time- and space-modulated nonlinearities.

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


Using similarity transformations we construct explicit nontrivial solutions of nonlinear Schrödinger equations with potentials and nonlinearities depending both on time and on the spatial coordinates. We present the general theory and use it to calculate explicitly nontrivial solutions such as periodic (breathers), resonant, or quasiperiodically oscillating solitons. Some implications to the field of matter waves are also discussed.

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