Soliton interactions and asymptotic state analysis in a discrete nonlocal nonlinear self-dual network equation of reverse-space type

doi:10.1088/1674-1056/abc2ba

Abstract We propose a reverse-space nonlocal nonlinear self-dual network equation under special symmetry reduction, which may have potential applications in electric circuits. Nonlocal infinitely many conservation laws are constructed based on its Lax pair. Nonlocal discrete generalized (m, N-m)-fold Darboux transformation is extended and applied to solve this system. As an application of the method, we obtain multi-soliton solutions in zero seed background via the nonlocal discrete N-fold Darboux transformation and rational solutions from nonzero-seed background via the nonlocal discrete generalized (1, N-1)-fold Darboux transformation, respectively. By using the asymptotic and graphic analysis, structures of one-, two-, three-and four-soliton solutions are shown and discussed graphically. We find that single component field in this nonlocal system displays unstable soliton structure whereas the combined potential terms exhibit stable soliton structures. It is shown that the soliton structures are quite different between discrete local and nonlocal systems. Results given in this paper may be helpful for understanding the electrical signals propagation.

Keywords: reverse-space nonlocal nonlinear self-dual network equation nonlocal discrete generalized (mN-m)-fold Darboux transformation multi-soliton solutions rational solutions

Received: 17 September 2020
Revised: 03 October 2020
Accepted manuscript online: 20 October 2020

PACS:	02.30.Ik	(Integrable systems)
	05.45.Yv	(Solitons)
	04.60.Nc	(Lattice and discrete methods)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 12071042 and 61471406), the Beijing Natural Science Foundation, China (Grant No. 1202006), and Qin Xin Talents Cultivation Program of Beijing Information Science and Technology University (QXTCP-B201704).

Corresponding Authors: ^†Corresponding author. E-mail: xiaoyongwen@163.com

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Cui-Lian Yuan(袁翠连) and Xiao-Yong Wen(闻小永) Soliton interactions and asymptotic state analysis in a discrete nonlocal nonlinear self-dual network equation of reverse-space type 2021 Chin. Phys. B 30 030201

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Soliton interactions and asymptotic state analysis in a discrete nonlocal nonlinear self-dual network equation of reverse-space type

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