### Abstract

In this paper, the pattern of the soliton solutions to the discrete nonlinear Schrödinger (DNLS) equations in a 2. D lattice is studied by the construction of horseshoes in l∞-spaces. The spatial disorder of the DNLS equations is the result of the strong amplitudes and stiffness of the nonlinearities. The complexity of this disorder is log(N+1) where N is the number of turning points of the nonlinearities. For the case N=1, there exist disjoint intervals I0 and I1, for which the state um,n at site (m,n) can be either dark (um,n∈I0) or bright (um,n∈I1) that depends on the configuration km,n=0 or 1, respectively. Bright soliton solutions of the DNLS equations with a cubic nonlinearity are also discussed.

Original language | English |
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Pages (from-to) | 736-749 |

Number of pages | 14 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 415 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2014 Jul 15 |

### Keywords

- Bright solitons
- Discrete nonlinear schrödinger equation
- Horseshoe
- Soliton solution
- Spatial disorder

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics