2022/08/30 by H. Sarfraz, Sarfraz, H., U. Saleem +3
Physics and Astronomy · #Discrete Mathematics (cs.DM) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Computer and information sciences #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2209.00738
openalex publication_date 2022/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, a fully discrete short pulse (SP) equation is presented as an integrability condition of a linear system of difference equations (also known as discrete Lax pair). Additionally, two semi-discrete versions of the SP equation have also been obtained from fully discrete SP equation under continuum limits. Darboux transformation is employed to compute multi-soliton solutions of fully discrete and semi-discrete SP equations. Explicit expressions of first and second nontrivial soliton solutions are computed. We also derived explicit expression of breather solution for fully discrete SP equation. The dynamics of single loop soliton and interaction mechanism of loop-loop and loop-antiloop solutions has been explored and illustrated.