Multi-peak breather stability in a dissipative discrete Nonlinear Schrödinger (NLS) equation
نویسندگان
چکیده
We study the stability of breather solutions of a dissipative cubic discrete NLS with localized forcing. The breathers are similar to the ones found for the Hamiltonian limit of the system. In the case of linearly stable multi-peak breathers the combination of dissipation and localized forcing also leads to stability, and the apparent damping of internal modes that make the energy around multi-peak breathers nondefinite. This stabilizing effect is however accompanied by overdamping for relatively small values of the dissipation parameter, and the appearance of near-zero stable eigenvalues.
منابع مشابه
Global Existence and Compact Attractors for the Discrete Nonlinear Schrödinger equation
We study the asymptotic behavior of solutions of discrete nonlinear Schrödinger-type (DNLS) equations. For a conservative system, we consider the global in time solvability and the question of existence of standing wave solutions. Similarities and differences with the continuous counterpart (NLS-partial differential equation) are pointed out. For a dissipative system we prove existence of a glo...
متن کاملExact Moving Breather Solutions of a Generalized Discrete Nonlinear Schrödinger Equation
We obtain exact moving breather solutions of a generalized discrete nonlinear Schrödinger equation. For finite lattices, we find two different moving periodic breather solutions while for an infinite lattice we find a localized moving breather solution.
متن کاملNumerical investigation of stability of breather-type solutions of the nonlinear Schrödinger equation
In this article we conduct a broad numerical investigation of stability of breather-type solutions of the nonlinear Schrödinger (NLS) equation, a widely used model of rogue wave generation and dynamics in deep water. NLS breathers rising over an unstable background state are frequently used to model rogue waves. However, the issue of whether these solutions are robust with respect to the kind o...
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 کاملBreather solutions of the discrete p-Schrödinger equation
We consider the discrete p-Schrödinger (DpS) equation, which approximates small amplitude oscillations in chains of oscillators with fully-nonlinear nearest-neighbors interactions of order α = p − 1 > 1. Using a mapping approach, we prove the existence of breather solutions of the DpS equation with evenor oddparity reflectional symmetries. We derive in addition analytical approximations for the...
متن کامل