https://doi.org/10.1140/epjp/s13360-021-01544-3
Regular Article
A new model with solitary waves: solution, stability and quasinormal modes
1
Condensed Matter Physics, Institute of Nuclear Physics, Polish Academy of Sciences, ul. W. E. Radzikowskiego 152, 31342, Kraków, Poland
2
Department of Physics, Indian Institute of Technology, 721 302, Kharagpur, India
Received:
22
March
2021
Accepted:
6
May
2021
Published online:
2
June
2021
We construct solitary wave solutions in a 
-dimensional massless scalar (
) field theory with a specially chosen potential 
. The equation governing perturbations about this solitary wave has an effective potential which is a simple harmonic well over a region, and a constant beyond. This feature allows us to ensure the stability of the solitary wave through the existence of bound states in the well, which can be found by semi-analytical methods. A further check on stability is performed through our search for quasi-normal modes (QNM) which are defined for purely outgoing boundary conditions. The time-domain profiles of the perturbations and the parametric variation of the QNM values are presented and discussed in some detail. Expectedly, a damped oscillatory temporal behaviour (ringdown) of the fluctuations is clearly seen through our analysis of the quasi-normal modes.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021
