TY - JOUR

T1 - Exact localized solutions of quintic discrete nonlinear Schrödinger equation

AU - Maruno, Ken Ichi

AU - Ohta, Yasuhiro

AU - Joshi, Nalini

N1 - Funding Information:
K.M. thanks Y. Kivshar, N. Akhmediev, A. Ankiewicz, K. Kajiwara, S.-I. Gotou, M. Oikawa and T. Tsuchida for useful suggestions. K.M. was supported by a JSPS Fellowship for Young Scientists. K.M. and Y.O. thank University of Sydney for warm hospitality. N.J.'s research was supported by the Australian Research Council.

PY - 2003/5/12

Y1 - 2003/5/12

N2 - We study a new quintic discrete nonlinear Schrödinger (QDNLS) equation which reduces naturally to an interesting symmetric difference equation of the form φn+1 + φn-1 = F(φn). Integrability of the symmetric mapping is checked by singularity confinement criteria and growth properties. Some new exact localized solutions for integrable cases are presented for certain sets of parameters. Although these exact localized solutions represent only a small subset of the large variety of possible solutions admitted by the QDNLS equation, those solutions presented here are the first example of exact localized solutions of the QDNLS equation. We also find chaotic behavior for certain parameters of nonintegrable case.

AB - We study a new quintic discrete nonlinear Schrödinger (QDNLS) equation which reduces naturally to an interesting symmetric difference equation of the form φn+1 + φn-1 = F(φn). Integrability of the symmetric mapping is checked by singularity confinement criteria and growth properties. Some new exact localized solutions for integrable cases are presented for certain sets of parameters. Although these exact localized solutions represent only a small subset of the large variety of possible solutions admitted by the QDNLS equation, those solutions presented here are the first example of exact localized solutions of the QDNLS equation. We also find chaotic behavior for certain parameters of nonintegrable case.

KW - Discrete solitons

KW - Hirota method

KW - Singularity confinement

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U2 - 10.1016/S0375-9601(03)00499-7

DO - 10.1016/S0375-9601(03)00499-7

M3 - Article

AN - SCOPUS:0037905066

VL - 311

SP - 214

EP - 220

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 2-3

ER -