Nonlocal conservation laws, nonlocal symmetries and exact solutions of an integrable soliton equation

Subhankar Sil, T. Raja Sekhar and Dia Zeidan

Chaos, Solitons & Fractals, 2020, vol. 139, issue C

Abstract: We compute nonlocal symmetries and obtain kink type soliton solutions to an integrable soliton equation. We construct a tree of nonlocally related partial differential equations (PDEs) of integrable soliton equation which consists of potential systems arising from conservation laws based method and inverse potential systems (IPS) from symmetry based method. We show that the integrable soliton equation admits two nonlocal symmetries among these one of which results from potential system and the other from locally related subsystem of IPS. We propose a systematic procedure to obtain exact solutions of a given PDE system using nonlocal symmetry which arises from IPS or its locally related subsystem. Finally, we obtain exact solutions to integrable soliton equation using nonlocal symmetries and discuss the physical behavior of the explicit solution graphically.

Keywords: Nonlocal symmetries; Nonlocally related PDE systems; Nonlocal conservation laws; Exact solutions; Soliton equation; Kink type soliton (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:139:y:2020:i:c:s0960077920304082

DOI: 10.1016/j.chaos.2020.110010

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