Solutions and continuum limits to nonlocal discrete sine‐Gordon equations: Bilinearization reduction method
Xiao‐bo Xiang, Song‐lin Zhao, Ying Shi
Abstract
Abstract In this paper, we investigate local and nonlocal reductions of a discrete negative order Ablowitz–Kaup–Newell–Segur equation. By the bilinearization reduction method, we construct exact solutions in double Casoratian form to the reduced nonlocal discrete sine‐Gordon equations. Then, nonlocal semidiscrete sine‐Gordon equations and their solutions are obtained through the continuum limits. The dynamics of soliton solutions are analyzed and illustrated by asymptotic analysis. The research ideas and methods in this paper can be generalized to other nonlocal discrete integrable systems.
Topics & Concepts
Integrable systemMathematicsMathematical physicsReduction (mathematics)SineSolitonMathematical analysisPhysicsClassical mechanicsNonlinear systemQuantum mechanicsGeometryNonlinear Waves and SolitonsNonlinear Photonic SystemsQuantum Mechanics and Non-Hermitian Physics