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

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  • Chiara Zanini
  • Fabio Zanolin

Abstract

We prove the existence and multiplicity of periodic solutions as well as solutions presenting a complex behavior for the one-dimensional nonlinear Schrödinger equation where the potential approximates a two-step function. The term generalizes the typical - 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 Poincaré map. We discuss the periodic and the Neumann boundary conditions. The value of the term although small, can be explicitly estimated.

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  • Chiara Zanini & Fabio Zanolin, 2018. "Complex Dynamics in One-Dimensional Nonlinear Schrödinger Equations with Stepwise Potential," Complexity, Hindawi, vol. 2018, pages 1-17, December.
    • Handle: RePEc:hin:complx:2101482
    DOI: 10.1155/2018/2101482
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    1. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
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