ANALYTICAL SOLUTIONS OF THE THERMODYNAMIC POTENTIAL OF THE MICHELSON MODEL IN EQUILIBRIUM SYSTEMS

The paper investigates exact solutions of a nonlinear fourth-order differential equation that follows from the variational principle for a thermodynamic potential with high derivatives. It is shown that certain classes of solutions can be represented by elliptic Jacobi functions of the delta-amplitude and elliptic cosine types, and in limiting cases – by localised Bell solitons. The conditions for the existence of real solutions are analyzed, and a relationship between the parameters of the equation and phase transitions to modulated states is established. In particular, the critical temperatures of second-order transitions corresponding to the emergence of modulated phases (MS1, MS2) are determined, and restrictions on the parameters of the thermodynamic potential are given. The results obtained are consistent with previous works and deepen the understanding of equilibrium states in systems with strong nonlinearity.