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Hybrid relativistic and modified Toda lattice-type system: equivalent form, N-fold Darboux transformation and analytic solutions

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Abstract

Studies of the lattice systems are of current interest due to their applications in relativity, optics, condensed matter physics and plasma physics. In this paper, we look into a hybrid relativistic and modified Toda lattice-type system. An equivalent form of that system is provided by virtue of certain transformations. Based on the Lax pair of that equivalent form, we construct an N-fold Darboux matrix and then derive the N-fold Darboux transformation, where N is a positive integer. Some analytic solutions are determined with the help of the associated N-fold Darboux transformation.

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Notes

  1. Investigations on certain nonlinear waves of the continuous nonlinear systems have been shown, e.g., in Refs. [11,12,13,14,15,16,17,18,19,20].

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Acknowledgements

We express our sincere thanks to the Editors and Reviewers for their valuable comments. This work has been supported by the National Natural Science Foundation of China under Grant Nos. 11772017, 11272023 and 11471050, by the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), China (IPOC: 2017ZZ05), by the Fundamental Research Funds for the Central Universities of China under Grant No. 2011BUPTYB02 and by the BUPT Excellent Ph.D. Students Foundation (No. CX2022156).

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Authors and Affiliations

  1. State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Yuan Shen, Bo Tian, Dan-Yu Yang & Tian-Yu Zhou

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  1. Yuan Shen
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  2. Bo Tian
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  3. Dan-Yu Yang
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Correspondence to Yuan Shen or Bo Tian.

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Shen, Y., Tian, B., Yang, DY. et al. Hybrid relativistic and modified Toda lattice-type system: equivalent form, N-fold Darboux transformation and analytic solutions. Eur. Phys. J. Plus 138, 744 (2023). https://doi.org/10.1140/epjp/s13360-023-04331-4

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