| Soliton interactions and asymptotic state analysis in a discrete nonlocal nonlinear self-dual network equation of reverse-space type |
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| 作者姓名： | 袁翠连 闻小永 |
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| 作者单位： | School of Applied Science |
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| 基金项目： | Project supported by the National Natural Science Foundation of China(Grant Nos.12071042 and 61471406);the Beijing Natural Science Foundation,China(Grant No.1202006);Qin Xin Talents Cultivation Program of Beijing Information Science and Technology University(QXTCP-B201704). |
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| 摘 要： | 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.
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| 关 键 词： | reverse-space nonlocal nonlinear self-dual network equation nonlocal discrete generalized(m N?m)-fold Darboux transformation multi-soliton solutions rational solutions |
Soliton interactions and asymptotic state analysis in a discrete nonlocal nonlinear self-dual network equation of reverse-space type |
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| Cui-Lian Yuan,Xiao-Yong Wen.Soliton interactions and asymptotic state analysis in a discrete nonlocal nonlinear self-dual network equation of reverse-space type[J].Chinese Physics B,2021(3). |
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| Authors: | Cui-Lian Yuan Xiao-Yong Wen |
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| Institution: | (School of Applied Science,Beijing Information Science and Technology University,Beijing 100192,China) |
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| 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. |
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