Integrable nonlinear ladder system with background-controlled intersite resonant coupling

摘要: A new spectral problem on one-dimensional lattices is found allowing consistently to support the zero-curvature representation for a wide class of integrable nonlinear ladder systems. The modified recurrence technique obtaining an infinite set conservation laws developed and some basic conserved quantities are explicitly derived. eigenvalue problems associated with limiting operator special case rapidly vanishing boundary conditions Schrodinger-type fields finite background condition concomitant field solved domains analyticity Jost functions presented both analytically graphically. This particular example shows that original auxiliary basically fourth order must generate four distinct have be involved in procedure inverse scattering transform. Moreover, there exists critical value accompanying which separates two principally different possibilities organization functions. crossover should inevitably lead qualitative rearrangements structure model solutions. Thus already limit low-amplitude excitations we strictly observe loss stability regarding linear spectrum Schrodinger subsystem just above practically unexcited field, whereas region essentially controlled by magnitude level via effective modification intersite resonant coupling self-site coupling.