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Degenerate solitons and asymptotic analysis for a three-coupled fourth-order nonlinear Schr?dinger system in an alpha helical protein |
| Dan-Yu Yang(杨丹玉)† |
| School of Mathematical Sciences, University of Jinan, Jinan 250022, China |
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Abstract We investigate the alpha helical protein structure characterized by fourth-order interspine coupling, focusing on a three-coupled fourth-order nonlinear Schröinger system. We introduce a generalized Darboux transformation, departing from the classical Darboux transformation. Based on this, we construct the two- and three-degenerate soliton solutions and four-degenerate asymptotic soliton solutions. Based on the asymptotic analysis, we find that the amplitudes of interacting solitons are retained upon the interactions. Elastic interactions between two degenerate solitons exhibiting four curve-type asymptotic solitons are depicted. When the lattice parameter $\beta$ changes, the velocities of the two degenerate solitons also change. Elastic interaction among three degenerate solitons comprising four curve-type asymptotic solitons and two line-type solitons is presented. Interaction among one soliton and two degenerate solitons with different velocities is shown. Elastic interaction among four degenerate solitons comprising eight curve-type asymptotic solitons is also presented. Interaction among two two-degenerate solitons with two spectral parameters is shown. The relative distance between two asymptotic solitons exhibits logarithmic growth with $|t|$, where $t$ represents the retarded time. Acceleration of soliton separation decays exponentially with relative distance, and eventually approaches zero. Phase shifts depend on $t$.
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Received: 30 April 2025
Revised: 19 June 2025
Accepted manuscript online: 28 July 2025
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PACS:
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02.30.Jr
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(Partial differential equations)
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02.30.Rz
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(Integral equations)
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94.05.Fg
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(Solitons and solitary waves)
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| Fund: This work is supported by the Natural Science Foundation of Shandong Province (Grant No. ZR2025QC30). |
Corresponding Authors:
Dan-Yu Yang
E-mail: ss_yangdy@163.com
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Cite this article:
Dan-Yu Yang(杨丹玉) Degenerate solitons and asymptotic analysis for a three-coupled fourth-order nonlinear Schr?dinger system in an alpha helical protein 2026 Chin. Phys. B 35 020201
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