Lie symmetries, qualitative analysis and exact solutions of nonlinear Schrödinger equations with inhomogeneous nonlinearities

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March 2008, 9(2): 221-233. doi: 10.3934/dcdsb.2008.9.221

Lie symmetries, qualitative analysis and exact solutions of nonlinear Schrödinger equations with inhomogeneous nonlinearities

Juan Belmonte-Beitia ^1, , Víctor M. Pérez-García ^2, , Vadym Vekslerchik ^2, and Pedro J. Torres ^3,

1.	Departamento de Matemáticas, E.T.S.I Industriales & Instituto de Matemática Aplicada a la Ciencia y la Ingeniería (IMACI), Avda. de Camilo José Cela, 3 Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain
2.	Departamento de Matemáticas, E.T.S.I. Industriales, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain
3.	Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada Campus de Fuentenueva s/n, 18071 Granada, Spain

Received March 2007 Revised November 2007 Published December 2007

Abstract
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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 study different examples and use the qualitative theory of dynamical systems to obtain some properties of these solutions.

Keywords: Nonlinear Schrodinger equations, dynamical systems., Solitons, Lie symmetries.

Mathematics Subject Classification: 35Q51, 35Q55, 34C1.

Citation: Juan Belmonte-Beitia, Víctor M. Pérez-García, Vadym Vekslerchik, Pedro J. Torres. Lie symmetries, qualitative analysis and exact solutions of nonlinear Schrödinger equations with inhomogeneous nonlinearities. Discrete & Continuous Dynamical Systems - B, 2008, 9 (2) : 221-233. doi: 10.3934/dcdsb.2008.9.221

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