In this paper, the maximal dissipative extensions of a symmetric singular 1D discrete Hamiltonian operator with maximal deficiency indices (2,2) (in limit-circle cases at ±∞) and acting in the Hilbert space ℓ_{Ω}²(Z;C²) (Z:={0,±1,±2,...}) are considered. We consider two classes dissipative operators with separated boundary conditions both at -∞ and ∞. For each of these cases we establish a self...

The concept of the dissipative soliton has received wide recognition in optics (physics in general), biology and medicine [Akhmediev & Ankiewicz, 2005, 2008]. This concept allows many diverse phenomena in nature to be understood and studied in a simple and systematic way. It represents a unifying notion in science, since it stresses common features in a variety of complicated behaviors of self-...

The basic stages of development of the theory of superconductivity are traced. Despite of remarkable successes of theory, the physical explanation of the phenomenon of superconductivity-of the not fading electrical current in dissipative medium-is not exists until now. In the present paper on the basis of works (Klimontovich, 1990abc, 1999) the physical explanations of this phenomenon is consid...