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Novel solitons and higher-order solitons for the nonlocal generalized Sasa–Satsuma equation of reverse-space-time type

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Abstract

The general soliton solutions and higher-order soliton solutions for the nonlocal generalized Sasa–Satsuma (SS) equation of reverse-space-time type are explored. Firstly, a novel nonlocal generalized SS equation is derived, and the infinitely many conserved quantities and conservation laws are considered. Secondly, some novel symmetry properties and nonlocal constraints for eigenvalues, eigenvectors and scattering data are obtained, which is quite different from the local ones. Then, in the framework of the Riemann–Hilbert problem and by the special nonlocal properties, the N-soliton formula with determinant and the higher-order soliton formulas are constructed for the nonlocal generalized SS equation by a limit technique. Thirdly, some new patterns and unusual dynamical behaviors of the N-soliton and the higher-order soliton solutions for the nonlocal generalized SS equation are exhibited and explored. The general single soliton is always collapsing periodically whether the eigenvalues are pure imaginary or not, but when the absolute value of the eigenvalue approaches to zero, the solution tends to be a standing solution, which does not move with time. Besides, some novel interesting physical patterns for the two-soliton solution are obtained, such as a singular wave in the periodical background and two-soliton solution with two singular branches. It is worth mentioning that the two-soliton solution does not degenerate into a bounded breathing soliton instead of a breathing singular wave when \(\lambda _{\scriptscriptstyle 2}=-\lambda _{\scriptscriptstyle 1}^*\). And the higher-order soliton with one double zero is singular and collapsing periodically while the soliton with triple zero is nonsingular when the eigenvalue is purely imaginary. query Please check the edit made in the article title.

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Data availability

The datasets generated and analyzed during the current study are available from the corresponding author on reasonable request.

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Funding

The work is supported by the Future Scientist and Outstanding Scholar Cultivation Program of East China Normal University (No.WLKXJ202001), National Natural Science Foundation of China(No.12175069) and Science and Technology Commission of Shanghai Municipality (No. 21JC1402500 and No. 18dz2271000).

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Authors and Affiliations

  1. Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, School of Mathematical Sciences, East China Normal University, Shanghai, 200241, China

    Minmin Wang & Yong Chen

  2. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, China

    Yong Chen

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  1. Minmin Wang
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All authors contributed to the study conception and theory. Calculation and analysis were performed by Wang Minmin. The first draft of the manuscript was written by Wang Minmin, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Yong Chen.

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The work was supported by the Future Scientist and Outstanding Scholar Cultivation Program of East China Normal University (No. WLKXJ202001), National Natural Science Foundation of China (No. 12175069) and Science and Technology Commission of Shanghai Municipality (No. 21JC1402500 and No. 18dz2271000).

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Wang, M., Chen, Y. Novel solitons and higher-order solitons for the nonlocal generalized Sasa–Satsuma equation of reverse-space-time type. Nonlinear Dyn 110, 753–769 (2022). https://doi.org/10.1007/s11071-022-07663-5

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