TY - JOUR

T1 - Characterization of soliton solutions in 2D nonlinear Schrödinger lattices by using the spatial disorder

AU - Shieh, Shih Feng

N1 - Funding Information:
The author appreciates the anonymous referee for the valuable comments and suggestions. This work is partially supported by the National Science Council .

PY - 2014/7/15

Y1 - 2014/7/15

N2 - 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.

AB - 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.

KW - Bright solitons

KW - Discrete nonlinear schrödinger equation

KW - Horseshoe

KW - Soliton solution

KW - Spatial disorder

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U2 - 10.1016/j.jmaa.2014.02.003

DO - 10.1016/j.jmaa.2014.02.003

M3 - Article

AN - SCOPUS:84896318890

SN - 0022-247X

VL - 415

SP - 736

EP - 749

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -