Spatial Disorder of Soliton Solutions for 2D Nonlinear Schrödinger Lattices
نویسنده
چکیده
In this paper, we employ the construction of topological horseshoes to study the pattern of the soliton solutions to the discrete nonlinear Schrödinger (DNLS) equations in a twodimensional 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.
منابع مشابه
Exact solutions of the Saturable Discrete Nonlinear Schrödinger Equation
Exact solutions to a nonlinear Schrödinger lattice with a saturable nonlinearity are reported. For finite lattices we find two different standing-wave-like solutions, and for an infinite lattice we find a localized soliton-like solution. The existence requirements and stability of these solutions are discussed, and we find that our solutions are linearly stable in most cases. We also show that ...
متن کاملTopological soliton solutions of the some nonlinear partial differential equations
In this paper, we obtained the 1-soliton solutions of the symmetric regularized long wave (SRLW) equation and the (3+1)-dimensional shallow water wave equations. Solitary wave ansatz method is used to carry out the integration of the equations and obtain topological soliton solutions The physical parameters in the soliton solutions are obtained as functions of the dependent coefficients. Note t...
متن کاملnew analytical method based on Riccati equation for finding Soliton solutions of Nonlinear Lakshmanan-Porsezian-Daniel (LPD) equation
In this present study analytical method based on Riccati Equation as for converting the Nonlinear Lakshmanan-Porsezian-Daniel (LPD) equation into the nonlinear ODE and finding soliton solutions of this sustem discused. Obtaining solutions are new and obtained from wave transformation. The obtained results show that the presented method is effective and appropriate for solving nonlinear differen...
متن کاملMulti soliton solutions, bilinear Backlund transformation and Lax pair of nonlinear evolution equation in (2+1)-dimension
As an application of Hirota bilinear method, perturbation expansion truncated at different levels is used to obtain exact soliton solutions to (2+1)-dimensional nonlinear evolution equation in much simpler way in comparison to other existing methods. We have derived bilinear form of nonlinear evolution equation and using this bilinear form, bilinear Backlund transformations and construction of ...
متن کاملGap Solitons in Periodic Discrete Nonlinear Schrödinger Equations
It is shown that the periodic DNLS, with cubic nonlinearity, possesses gap solutions, i. e. standing waves, with the frequency in a spectral gap, that are exponentially localized in spatial variable. The proof is based on the linking theorem in combination with periodic approximations. Mathematics subject classification: 35Q55, 35Q51, 39A12, 39A70, 78A40
متن کامل