Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities |
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| Authors: | Belmonte-Beitia Juan Pérez-García Víctor M Vekslerchik Vadym Torres Pedro J |
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| Institution: | 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. |
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| Abstract: | Using Lie group theory and canonical transformations, we construct explicit solutions of nonlinear Schr?dinger 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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