Peculiarities of oscillator with nonlinear cordinate-dependent mass

TL;DR

This paper introduces a nonlinear scalar field model with coordinate-dependent mass, capable of describing phase transitions with inhomogeneous order parameters, and provides exact solutions relevant to physical phenomena like spinodal decomposition and cosmology.

Contribution

The paper develops a novel nonlinear scalar field model with gradient coupling and exact solutions, linking it to physical processes such as phase transitions and confinement.

Findings

Model describes phase transition with inhomogeneous order parameter

Exact analytical solutions are obtained for specific energy values

Predictions are experimentally verifiable

Abstract

A nonlinear model of the scalar field with a coupling between the field and its gradient is developed. It is shown, that such model is suitable for the description of phase transition accompanied by formation of spatial inhomogeneous distribution of the order parameter. The proposed model is analogous the mechanical nonlinear oscillator with the coordinate-dependent mass or velocity-dependent elastic module. Besides, for some value of energy the model under consideration possesses exact analytical solution. We assume that this model can related to the spinodal decomposition, quark confinement, or cosmological scenario. All predictions can be verified experimentally.