Coupling-governed metamorphoses of the integrable nonlinear Schrödinger system on a triangular-lattice ribbon

Semidiscrete Integrable Nonlinear Schrӧdinger System with Background-Controlled Intersite Resonant Coupling. Short Summary of Key Properties

“…As a consequence, the primary integrable nonlinear system with appropriately adjusted parametrical driving becomes isomorphic to the system modeling the Bloch oscillations of charged nonlinear carriers in the electrically biased ribbon of a triangular lattice. The justification of this statement can be found in our recent paper [37].…”

“…In the referred review articles [41,42], we considered the most important properties of the semidiscrete integrable nonlinear Schrödinger system with background-controlled intersite resonant coupling in view of a significant role that the semidiscrete integrable models of the nonlinear Schrödinger-type play in the description of different phenomena from various branches of physics. The core of reviewed results [41,42] lies in eight original articles [32,[34][35][36][37][38][39][40], though the impact of works [17,27,28] dealing with the standardization of the famous Ablowitz-Ladik semidiscrete nonlinear system seems to be indispensable. As the matter of fact, author's activity in the standardization of the Ablowitz-Ladik system [27,28] has been inspired by the rather critical attitude of Professor A.S. Davydov toward the nonstandard field amplitudes as those lacking the direct physical sense [33].…”

“…Having been written in terms of two pairs of basic field amplitudes + ( ), + ( ) and − ( ), − ( ) accompanied by one pair of concomitant field amplitudes ( ), ( ), the dynamics of the integrable nonlinear Schrödinger system on a triangular-lattice ribbon is governed by the following set of equations [32,[35][36][37][38][39][40][41][42]:…”

“…Moreover, the coupling parameters are capable to incorporate the impact of an external linear potential on the dynamics of the primary system (2.1)-(2.6) via the appropriate modification of their time dependences [37]. The semidiscrete nonlinear system under study (2.1)-(2.6) permits the zero-curvature representatioṅ…”

“…In this respect, the semidiscrete integrable nonlinear Schrödinger system with background-controlled intersite resonant coupling [32,35,36] is able to find considerable physical applications as a multicomponent system with two types of free coupling parameters giving rise to rather unusual properties [37,38] and as a system, whose underlying lattice structure is closely related to that of (1,1) boron nanotube [18] belonging to the new class of lowdimensional synthetic materials known as nanoribbons [14,16,20]. The most representative results concerning this system have recently been published in our review articles [41,42].…”