2016/12/31 by Man Jia, M Jia, S Y Lou +1
Chemistry · Mathematics · Physics and Astronomy · #Chemistry #Geometry #Invariant (physics) #Korteweg–de Vries equation #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Parity (physics) #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Soliton #Symmetry (geometry) #Symmetry breaking #Transformation (genetics) #nlin.SI
paper · pdf · doi:10.1016/j.physleta.2018.02.036
published as Physics Letters A 382 (2018) 1157-1166 · 20 pages
openalex publication_date 2018/03/05 · openalex created_date 2018/03/29 · arxiv created 2022/02/22 · arxiv updated 2022/02/23 · openalex updated_date 2026/08/05
In natural and social science, many events happened at different space-times may be closely correlated. Two events, A (Alice) and B (Bob) are defined as correlated if one event is determined by another, say, B=f A for suitable f operators. A nonlocal AB-KdV system with shifted-parity (Ps, parity with a shift), delayed time reversal (Td, time reversal with a delay) symmetry where B=PsTd A is constructed directly from the normal KdV equation to describe two-area physical event. The exact solutions of the AB-KdV system, including Ps Td invariant and Ps Td symmetric breaking solutions are shown by different methods. The Ps Td invariant solution show that the event happened at A will happen also at B. These solutions, such as single soliton solutions, infinitely many singular soliton solutions, soliton-cnoidal wave interaction solutions, and symmetry reduction solutions etc., show the AB-KdV system possesses rich structures. Also, a special Bäcklund transformation related to residual symmetry is presented via the localization of the residual symmetry to find interaction solutions between the solitons and other types of the AB-KdV system.