First-order framework and generalized global defect solutions

TL;DR

This paper introduces a new first-order framework for finding defect solutions in generalized scalar field models, extending the superpotential approach to models with modified kinetic terms and multiple fields.

Contribution

It develops a generalized first-order formalism for defect solutions in models with modified kinetic terms, applicable to multiple scalar fields, and provides explicit examples.

Findings

Established a new first-order framework for generalized models

Derived explicit defect solutions for single scalar field cases

Extended the superpotential method to non-standard kinetic models

Abstract

This work deals with defect structures in models described by scalar fields. The investigations focus on generalized models, with the kinetic term modified to allow for a diversity of possibilities. We develop a new framework, in which we search for first-order differential equations which solve the equations of motion. The main issue concerns the introduction of a new function, which works like the superpotential usually considered in the standard situation. We investigate the problem in the general case, with an arbitrary number of fields, and we present several explicit examples in the case of a single real scalar field.