Solitons of the Symmetric $\phi^4$-$\phi^2 |\phi|$-$\phi^2$ Triple Well Model

TL;DR

This paper explores the solutions of a symmetric triple well scalar field model, including kinks, pulses, and periodic solutions, and generalizes it to higher powers, providing a comprehensive analysis of its phase transition behavior.

Contribution

It introduces a generalized symmetric $\

Findings

Derived kink and pulse solutions for the model.

Presented periodic solutions for the model.

Extended analysis to generalized models with arbitrary powers.

Abstract

A symmetric $\phi^4$-$\phi^2 |\phi|$-$\phi^2$ model has recently attracted a lot of attention due to its usefulness in studying tunable phase transitions. We analyze the behavior of this model for the entire range of parameters and obtain its kink and pulse solutions. For completeness, we also present several periodic solutions of this model. Furthermore, we present a generalized symmetric $\phi^{4n}$-$\phi^{2n}|\phi|$-$\phi^2$ model where $n = 1, 2, 3, ...$ and obtain its kink and pulse solutions for arbitrary $n$.