2015/12/03 by D. I. Borisov, Borisov, Denis I., Sergey V. Dmitriev +1
Physics and Astronomy · #Advanced Fiber Laser Technologies #Analysis of PDEs (math.AP) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Spectral Theory (math.SP)
paper · pdf · doi:10.48550/arxiv.1512.01103
openalex publication_date 2015/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a series of recent works by Demirkaya et al. stability analysis for the\nstatic kink solutions to the 1D continuous and discrete Klein-Gordon equations\nwith a \PT-symmetric perturbation has been analysed. We consider the\nlinear stability problem for the static kink in 2D Klein-Gordon field taking\ninto account spatially localized \PT-symmetric perturbation. The\nperturbation is in the form of viscous friction, which does not affect the\nstatic solutions to the unperturbed Klein-Gordon equation. Small dynamic\nperturbation around the static kink solution is considered to formulate the\nlinear stability problem. The effect of the small perturbation on the solutions\nto the corresponding eigenvalue problem is analysed. The main result is\npresented in the form of a theorem describing the behavior of the eigenvalues\ncorresponding to the extended and localised eigenmodes as the functions of the\nperturbation parameter.\n