General solutions for some classes of interacting two field kinks

TL;DR

This paper introduces classes of coupled two-field models where the nonlinear equations can be linearized and solved exactly, bypassing the trial orbit method, with applications in defect networks and polymer physics.

Contribution

It presents new classes of models with linearizable coupled equations, enabling exact solutions without trial orbit methods.

Findings

Models can be solved exactly due to linearization.

Applicable to defect networks and polymer properties.

Simplifies analysis of certain physical systems.

Abstract

In this work we present some classes of models whose the corresponding two coupled first-order nonlinear equations can be put into a linear form, and consequently be solved completely. In these cases the so-called trial orbit method is completely unnecessary. We recall that some physically important models as, for instance, the problem of tiling a plane with a network of defects and polymer properties are in this class of models.