Stability in integrable nonlocal nonlinear equations

Abstract

Recently a variety of nonlocal integrable systems has been introduced that besides fields located at particlar space-time points simultaneously also contain fields that are located at different, but symmetrically related, points. Here we investigate different types of soliton solutions with regard to their stability against linear pertubations obtained for the nonlocal version of the Hirota/nonlinear Schrödinger equation and the so-called Alice and Bob versions of the Korteweg-de Vries and Bousinesq equations. We encounter different types of scenarios: Solition solutions that are linearly stable or unstable and also solutions that change their stability properties depending on the parameter regime they are in.

arXiv comment14 pages, 4 figures

References in corpus (7)

• Alice-Bob Physics: Coherent Solutions of Nonlocal KdV Systems
• Alice-Bob systems, $P_s$-$T_d$-$C$ principles and multi-soliton solutions
• PT-symmetric Deformations of the Korteweg-de Vries Equation
• Integrable nonlocal Hirota equations
• On Symmetries and Exact Solutions of a Class of Non-local Non-linear Schrodinger Equations with Self-induced PT-symmetric Potential
• Complex solitons with real energies
• Complex BPS solitons with real energies from duality