Abstract
The analogy between the Cooper pair in high temperature superconductor and the quark-antiquark pair in quantum chromodynamics (QCD) is proposed. In QCD the nonlinear chromodynamical field between a quark and an antiquark is confined to a tube. So we assume that there is the strong interaction between phonons which can confine them to some tube too. This tube is described using the nonlinear Schr\"odinger equation. We show that it has an infinite spectrum of axially symmetric (string) solutions with negative finite linear energy density. The one-dimensional nonlinear Schr\"odinger equation has a finite spectrum (hence, it has a steady-state) which describes the Cooper pair squezeed between anisotropy planes in the superconductor. It is shown that in this model the transition temperature is approximately 45 K.
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