Determinant Form of Dark Soliton Solutions of the Discrete Nonlinear Schrödinger Equation
نویسندگان
چکیده
It is shown that the N-dark soliton solutions of the integrable discrete nonlinear Schrödinger (IDNLS) equation are given in terms of the Casorati determinant. The conditions for reduction, complex conjugacy and regularity for the Casorati determinant solution are also given explicitly. The relationship between the IDNLS and the relativistic Toda lattice is discussed.
منابع مشابه
N -Bright-Dark Soliton Solution to a Semi-Discrete Vector Nonlinear Schrödinger Equation
In this paper, a general bright-dark soliton solution in the form of Pfaffian is constructed for an integrable semi-discrete vector NLS equation via Hirota’s bilinear method. Oneand two-bright-dark soliton solutions are explicitly presented for two-component semidiscrete NLS equation; two-bright-one-dark, and one-bright-two-dark soliton solutions are also given explicitly for three-component se...
متن کاملCasorati Determinant Form of Dark Soliton Solutions of the Discrete Nonlinear Schrödinger Equation
is one of most important soliton equations in mathematics and physics. The study of discrete analogues of the NLS equation has received considerable attention recently from both physical and mathematical point of view.1, 2 The integrable discrete nonlinear Schrödinger (IDNLS) equation is given by i dψn dt = ψn+1 + ψn−1 + α|ψn|(ψn+1 + ψn−1) . (1.2) The IDNLS equation was originally derived by Ab...
متن کاملOn existence of dark solitons in cubic-quintic nonlinear Schrödinger equation with a periodic potential
A proof of existence of stationary dark soliton solutions of the cubic-quintic nonlinear Schrödinger equation with a periodic potential is given. It is based on the interpretation of the dark soliton as a heteroclinic on the Poincaré map.
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 کاملClosed Form Solutions to the Integrable Discrete Nonlinear Schrödinger Equation
In this article we derive explicit solutions of the matrix integrable discrete nonlinear Schrödinger equation by using the inverse scattering transform and the Marchenko method. The Marchenko equation is solved by separation of variables, where the Marchenko kernel is represented in separated form, using a matrix triplet (A,B,C). Here A has only eigenvalues of modulus larger than one. The class...
متن کامل