Stationary Solitons in discrete NLS with non-nearest neighbour interactions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908898301050880 |
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| author | Rothos, Vassilis M. Anastassiou, Stavros Hadjifotinou, Katerina G. |
| author_facet | Rothos, Vassilis M. Anastassiou, Stavros Hadjifotinou, Katerina G. |
| contents | The aim of this paper is to provide a construction of stationary discrete solitons in an extended one-dimensional Discrete NLS model with non-nearest neighbour interactions. These models, models of the type with long-range interactions were studied in various other contexts. In particular, it was shown that, if the interaction strength decays sufficiently slowly as a function of distance, it gives rise to bistability of solitons, which may find applications in their controllable switching. Dynamical lattices with long-range interactions also serve as models for energy and charge transport in biological molecules. Using a dynamical systems method we are able to construct, with great accuracy, stationary discrete solitons for our model, for a large region of the parameter space. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_15088 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stationary Solitons in discrete NLS with non-nearest neighbour interactions Rothos, Vassilis M. Anastassiou, Stavros Hadjifotinou, Katerina G. Dynamical Systems Mathematical Physics Analysis of PDEs The aim of this paper is to provide a construction of stationary discrete solitons in an extended one-dimensional Discrete NLS model with non-nearest neighbour interactions. These models, models of the type with long-range interactions were studied in various other contexts. In particular, it was shown that, if the interaction strength decays sufficiently slowly as a function of distance, it gives rise to bistability of solitons, which may find applications in their controllable switching. Dynamical lattices with long-range interactions also serve as models for energy and charge transport in biological molecules. Using a dynamical systems method we are able to construct, with great accuracy, stationary discrete solitons for our model, for a large region of the parameter space. |
| title | Stationary Solitons in discrete NLS with non-nearest neighbour interactions |
| topic | Dynamical Systems Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2407.15088 |