Excitation spectra of solitary waves in scalar field models with polynomial self-interaction

TL;DR

This paper investigates the excitation spectra of solitary wave kinks in scalar field models with polynomial self-interaction, analyzing scattering, resonance phenomena, and long-range interactions through numerical simulations.

Contribution

It provides new insights into the resonance phenomena and long-range interactions of kinks in scalar field models with polynomial self-interaction.

Findings

Resonance phenomena linked to energy exchange between modes.

Long-range interactions observed in power-law asymptotic kinks.

Numerical analysis of kink scattering dynamics.

Abstract

We study excitations of solitary waves -- the kinks -- in scalar models with degree eight polynomial self-interaction in (1+1) dimensions. We perform numerical studies of scattering of two kinks with an exponential asymptotic off each other and analyse the occurring resonance phenomena. We connect these phenomena to the energy exchange between the translational and the vibrational modes of the colliding kinks. We also point out that the interaction of two kinks with power-law asymptotic can lead to a long-range interaction between the two kinks.