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High-Order Line-Soliton Interactions and Anomalous Scattering of Lumps in a (2+1)-Dimensional Reverse Space–Time Nonlinear Schrödinger Equation

Author

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  • Meng’en Wang

    (School of Physics, Beihang University, Beijing 100191, China)

  • Yichao Wang

    (School of Mathematical Sciences, Beihang University, Beijing 100191, China)

  • Guangmei Wei

    (School of Mathematical Sciences, Beihang University, Beijing 100191, China)

  • Haoqing Chen

    (School of Mathematical Sciences, Beihang University, Beijing 100191, China)

  • Chunrui Fu

    (School of Physics, Beihang University, Beijing 100191, China)

  • Hanyue Deng

    (School of Mathematical Sciences, Beihang University, Beijing 100191, China)

Abstract

This study presents a systematic investigation of nonlinear wave interactions in a (2+1)-dimensional nonlinear Schrödinger equation with a space–time-symmetric potential. We focus on the interaction dynamics of high-order line-soliton solutions and on the anomalous scattering phenomena exhibited by high-order lump solutions, which correspond to fully localized spatiotemporal optical wave packets. Using the generalized Darboux transformation, we obtain, for the first time, explicit high-order line-soliton solutions for this model. A rigorous asymptotic analysis framework is developed to characterize the behavior of these solutions on both long and short time scales. Furthermore, high-order lump solutions are constructed, and their decomposition and anomalous scattering properties are elucidated. This work provides new insights into complex wave dynamics in higher-dimensional integrable systems and their implications for multidimensional beam propagation in nonlinear optical media.

Suggested Citation

  • Meng’en Wang & Yichao Wang & Guangmei Wei & Haoqing Chen & Chunrui Fu & Hanyue Deng, 2026. "High-Order Line-Soliton Interactions and Anomalous Scattering of Lumps in a (2+1)-Dimensional Reverse Space–Time Nonlinear Schrödinger Equation," Mathematics, MDPI, vol. 14(9), pages 1-26, April.
    • Handle: RePEc:gam:jmathe:v:14:y:2026:i:9:p:1429-:d:1927388
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