Dynamical analysis and localized waves of the n-component nonlinear Schrödinger equation with higher-order effects

doi:10.1088/1674-1056/ada435

中国物理B ›› 2025, Vol. 34 ›› Issue (3): 30201-030201.doi: 10.1088/1674-1056/ada435

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Dynamical analysis and localized waves of the n-component nonlinear Schrödinger equation with higher-order effects

Yu Lou(娄瑜)^1,† and Guoan Xu(许国安)²

1 Public Basic Education Department, Zhejiang Industry Polytechnic College, Shaoxing 312000, China;
2 School of Mathematical Science, Huaqiao University, Quanzhou 362021, China

收稿日期:2024-10-26 修回日期:2024-12-04 发布日期:2025-02-18
通讯作者: Yu Lou E-mail:lyzjipc@163.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 12271096) and the Natural Science Foundation of Fujian Province (Grant No. 2021J01302).

Dynamical analysis and localized waves of the n-component nonlinear Schrödinger equation with higher-order effects

Yu Lou(娄瑜)^1,† and Guoan Xu(许国安)²

1 Public Basic Education Department, Zhejiang Industry Polytechnic College, Shaoxing 312000, China;
2 School of Mathematical Science, Huaqiao University, Quanzhou 362021, China

Received:2024-10-26 Revised:2024-12-04 Published:2025-02-18
Contact: Yu Lou E-mail:lyzjipc@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 12271096) and the Natural Science Foundation of Fujian Province (Grant No. 2021J01302).

摘要/Abstract

摘要： Under investigation is the $n$-component nonlinear Schrödinger equation with higher-order effects, which describes the ultrashort pulses in the birefringent fiber. Based on the Lax pair, the eigenfunction and generalized Darboux transformation are derived. Next, we construct several novel higher-order localized waves and classified them into three categories: (i) higher-order rogue waves interacting with bright/antidark breathers, (ii) higher-order breather fission/fusion, (iii) higher-order breather interacting with soliton. Moreover, we explore the effects of parameters on the structure, collision process and energy distribution of localized waves and these characteristics are significantly different from previous ones. Finally, the dynamical properties of these solutions are discussed in detail.

关键词: $n$-component nonlinear Schrödinger equation with higher-order effects, generalized Darboux transformation, localized waves, soliton, breather, rogue wave

Abstract: Under investigation is the $n$-component nonlinear Schrödinger equation with higher-order effects, which describes the ultrashort pulses in the birefringent fiber. Based on the Lax pair, the eigenfunction and generalized Darboux transformation are derived. Next, we construct several novel higher-order localized waves and classified them into three categories: (i) higher-order rogue waves interacting with bright/antidark breathers, (ii) higher-order breather fission/fusion, (iii) higher-order breather interacting with soliton. Moreover, we explore the effects of parameters on the structure, collision process and energy distribution of localized waves and these characteristics are significantly different from previous ones. Finally, the dynamical properties of these solutions are discussed in detail.

Key words: $n$-component nonlinear Schrödinger equation with higher-order effects, generalized Darboux transformation, localized waves, soliton, breather, rogue wave

中图分类号: (Integrable systems)

02.30.Ik

02.30.Jr (Partial differential equations) 05.45.Yv (Solitons)

Yu Lou(娄瑜) and Guoan Xu(许国安). Dynamical analysis and localized waves of the n-component nonlinear Schrödinger equation with higher-order effects[J]. 中国物理B, 2025, 34(3): 30201-030201.

Yu Lou(娄瑜) and Guoan Xu(许国安). Dynamical analysis and localized waves of the n-component nonlinear Schrödinger equation with higher-order effects[J]. Chin. Phys. B, 2025, 34(3): 30201-030201.

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Dynamical analysis and localized waves of the n-component nonlinear Schrödinger equation with higher-order effects

Dynamical analysis and localized waves of the n-component nonlinear Schrödinger equation with higher-order effects

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