Multi-peaked localized states of DNLS in one and two dimensions

Abstract

Multi-peaked localized stationary solutions of the discrete nonlinear Schrödinger (DNLS) equation are presented in one (1D) and two (2D) dimensions. These are excited states of the discrete spectrum and correspond to multi-breather solutions. A simple, very fast, and efficient numerical method, suggested by Aubry, has been used for their calculation. The method involves no diagonalization, but just iterations of a map, starting from trivial solutions of the anti-continuous limit. Approximate analytical expressions are presented and compared with the numerical results. The linear stability of the calculated stationary states is discussed and the structure of the linear stability spectrum is analytically obtained for relatively large values of nonlinearity.

Exact solution for polarons on the anharmonic lattice and charge transfer in biopolymers

“…Polarons with a fine structure (with several peaks superimposed on the general envelope) are yet unknown. In previously found so called "multipeak polarons," several spatially separated individual polarons are formed, each having a fraction of the total wave function; i.e., each polaron has a formally frac tional charge [42]. In our results, the wave function wholly belongs to one polaron, which is one of the important differences from previous results.…”

Discrete breathers — Advances in theory and applications

“…They were predicted and obtained by Christodoulides and Joseph [63]. In the uncoupled limit C = 0 (also known as anti-continuous limit [249,18]) these solutions asymptotically approach compact single-site or two-site excitations with one or two sites excited to the amplitude φ (0) = √ Ω b /γ and all the rest of the lattice amplitudes being exactly zero (see also [203,190]). Often these solutions are also coined site-centered and bond-centered DBs, respectively, referring to their spatial structures.…”

Discrete solitons in nonlinear Schrödinger lattices with a power-law nonlinearity

“…[26]: bound states of the FSs with opposite signs may be stable, while compounds built of in-phase fundamental solitons may be only unstable (see also Refs. [27], where multihumped complexes were studied in chain of coupled oscillators and the work of [28], where such states were examined in one and two dimensions for the cubic nonlinearity). In Section 4, we present a theoretical analysis for the stability of such multi-humped states, while in Section 5 we report numerical results for basic families of the bound states in the present system.…”