A new model with solitary waves: solution, stability and quasinormal modes

We construct solitary wave solutions in a \(1+1\)-dimensional massless scalar (\(\phi \)) field theory with specially chosen potential \(V(\phi )\). The equation governing perturbations about this has an effective which is simple harmonic well over region, and constant beyond. This feature allows us to ensure the stability of through existence bound states well, can be found by semi-analytical methods. A further check on performed our search for quasi-normal modes (QNM) are defined purely outgoing boundary conditions. time-domain profiles parametric variation QNM values presented discussed some detail. Expectedly, damped oscillatory temporal behaviour (ringdown) fluctuations clearly seen analysis modes.