We prove the existence and multiplicity of periodic solutions as well as solutions presenting a complex behavior for the one-dimensional nonlinear Schrodinger equation -epsilon 2u+V(x)u=f(u), where the potential V(x) approximates a two-step function. The term f(u) generalizes the typical p-power nonlinearity considered by several authors in this context. Our approach is based on some recent developments of the theory of topological horseshoes, in connection with a linked twist maps geometry, which are applied to the discrete dynamics of the Poincare map. We discuss the periodic and the Neumann boundary conditions. The value of the term epsilon>0, although small, can be explicitly estimated.

Complex Dynamics in One-Dimensional Nonlinear Schrödinger Equations with Stepwise Potential / Zanini, C.; Zanolin, Fabio. - In: COMPLEXITY. - ISSN 1076-2787. - 2018:(2018). [10.1155/2018/2101482]

Complex Dynamics in One-Dimensional Nonlinear Schrödinger Equations with Stepwise Potential

C. Zanini;ZANOLIN, FABIO
2018

Abstract

We prove the existence and multiplicity of periodic solutions as well as solutions presenting a complex behavior for the one-dimensional nonlinear Schrodinger equation -epsilon 2u+V(x)u=f(u), where the potential V(x) approximates a two-step function. The term f(u) generalizes the typical p-power nonlinearity considered by several authors in this context. Our approach is based on some recent developments of the theory of topological horseshoes, in connection with a linked twist maps geometry, which are applied to the discrete dynamics of the Poincare map. We discuss the periodic and the Neumann boundary conditions. The value of the term epsilon>0, although small, can be explicitly estimated.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11583/2750218
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