Partial Exact Solutions of Nonlinear Distribution One-Component Order Parameter in Equilibrium Systems
DOI:
https://doi.org/10.26565/2312-4334-2025-4-13Keywords:
Nonlinear differential equations, Order parameter, Elliptic Jacobi functions, First-order phase transition, Incommensurate phaseAbstract
This paper investigates partial exact solutions of a nonlinear fourth-order differential equation arising from the variational principle for a thermodynamic potential with high derivatives. To describe the spatial distribution of the order parameter, the elliptic cosine function of Jacobi is used, which allows reducing the problem to a system of algebraic equations for amplitude, spatial scale, and modulus. The conditions for the existence of physically admissible solutions were obtained, and it was found that periodic solutions expressed in terms of elliptic cosine are relevant for describing first-order phase transitions. Graphs illustrating the dependence of the main parameters of the solution on the characteristics of the system are presented.
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