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Shih-Feng Shieh

2010-03-25
15:30:00 - 16:30:00

Spatial disorder of soliton solutions for discrete nonlinear Schr\"odinger equations in a $2D$ lattice

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

In this talk, we employ the construction of topological horseshoes to study the pattern of the soliton solutions to the discrete nonlinear Schr\"odinger (DNLS) equations in a two-dimensional lattice. 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 determined by the oscillations (number of turning points) of the nonlinearities. Nonnegative soliton solutions of the DNLS equations with a cubic nonlinearity is also discussed.