Abstract

CABRERA, E; GONZALEZ-PEREZ-SANDI, S  and  FUJIOKA, J. From embedded solitons to 4d dynamical systems. Rev. mex. fis. [online]. 2007, vol.53, n.1, pp.47-57. ISSN 0035-001X.

Abstract The term "embedded soliton" was coined in 1999 to describe a new type of soliton (discovered in 1997) whose internal frequencies lie within the spectrum of the radiation modes of certain nonlinear systems. In 2005 it was discovered that "embedded lattice solitons" (ELS) can also exist in discrete systems. The present communication shows that a discrete higher-order NLS equation with exact ELS leads naturally to a four-dimensional dynamical system that can be cast in the form , where F is a nonlinear function. In all the particular cases studied in this communication, at least two of the four Lyapunov coefficients associated with the system are positive, thus indicating a chaotic behavior.

Keywords : Embedded solitons; lattice solitons; dynamical systems; discrete NLS equation; nonlinear Schrodinger equation.

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