Abstract
The fourth order linear differential equation is obtained for the probability density considering the non-Hermitian Hamiltonian (the case of quasistationary states—complexity of energy). Third order nonlinear differential equation for the square of the modulus of the order parameter and for the phase is obtained by making use of Ginzburg–Landau equations. Three integrals of “motion” are found in the absence of the external magnetic field and two integrals are found in the presence of the external magnetic field. The analysis of these integrals is conducted. New analytical solutions are obtained.
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