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Soliton Solutions of an Integrable Coupled Discrete Nonlocal Nonlinear Schrödinger Equation
- 1 College of Science, University of Shanghai for Science and Technology, Shanghai, China
* Author to whom correspondence should be addressed.
Abstract
This study employs Hirota’s bilinear method to derive exact solutions for the coupled discrete non-local nonlinear Schrödinger (NLS) equation. The equation under investigation is derived from the non-local reduction of the coupled discrete nonlinear NLS equation, which arises in various physical contexts such as nonlinear optics and Bose-Einstein condensates. Exact solutions of coupled discrete non-local NLS equations are obtained, including bright-bright one-soliton solutions, two-soliton solutions, and dark-dark soliton solutions. For the dark-dark soliton solution, the construction of the solution and the bilinear expansion are derived from the continuous system, but the continuous system solved in this way yields a breathing solution, however, in this coupled discrete non-local NLS equation, under specific parameters, we obtain coupled dark-dark soliton waves. In addition, periodic solutions, singular solutions and double spatial period solutions are obtained by taking different parameters. The soliton dynamics are visualized using mathematical software, providing insights into their behavior and interactions. This work enhances the understanding of soliton solutions in discrete non-local systems and provides a practical approach for analyzing similar nonlinear wave phenomena.
Keywords
Bilinear method, Coupled discrete nonlocal Schrödinger equation, Exact solutions
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Cite this article
Lv,M. (2025). Soliton Solutions of an Integrable Coupled Discrete Nonlocal Nonlinear Schrödinger Equation. Theoretical and Natural Science,106,1-9.
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The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.
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Volume title: Proceedings of the 3rd International Conference on Mathematical Physics and Computational Simulation
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