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<p>Lump and breather-type solutions have recently gained wide interest in nonlinear optics because of their fundamental importance in photonic systems and wave propagation studies. A lump soliton (LS) refers to a rationally localized wave that decays algebraically in every spatial direction, representing stable energy packets that remain confined without dispersing in optical media. In contrast, breather solutions (BS) describe waves that are localized in both space and time but display oscillatory behavior, either temporally or spatially, and they often serve as prototypes for nonlinear modulations and the generation of rogue waves. In this study, we consider a generalized wave propagation equation known as generalized Longitudinal Lugiato Lefever equation (gLLLE) which is capable of modeling both passive and active cavities, as well as hybrid structures such as semiconductor ring lasers subject to external optical driving. By employing suitable transformation techniques, we construct a variety of nonlinear excitations, including lump, lump–one strip (LoS), lump–two strip (LtS), lump–periodic (LP), and rogue wave solutions, together with several interaction patterns involving lumps, periodic waves, and kink waves. Moreover, we compute several families of breather solutions, such as Ma breathers (MBs), Kuznetsov-Ma breathers (KMBs), generalized breathers (GBs), and Akhmediev breathers (ABs), together with their associated rogue waves, and depict their structures using 3D, 2D, and contour plots. The outcomes of this study carry strong practical relevance, as lump and breather dynamics underpin applications in optical communication, all-optical switching, ultra-fast pulse generation, and secure information transfer. Furthermore, understanding their interactions sheds light on controlling extreme optical events like rogue waves, which is crucial for the stability of high-power laser systems and fiber-optic networks. Overall, our results offer new insights into the interplay of localized and periodic wave structures, paving the way for advances in integrated photonics, nonlinear optical systems, and next-generation telecommunication technologies.</p>

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Structure of breathers and lump solutions for generalized Longitudinal Lugiato Lefever equation in externally-driven ring lasers

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月22日

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  • Sarfaraz Ahmed,
  • Ibtehal Alazman,
  • Syed T. R. Rizvi,
  • Aly R. Seadawy

摘要

Lump and breather-type solutions have recently gained wide interest in nonlinear optics because of their fundamental importance in photonic systems and wave propagation studies. A lump soliton (LS) refers to a rationally localized wave that decays algebraically in every spatial direction, representing stable energy packets that remain confined without dispersing in optical media. In contrast, breather solutions (BS) describe waves that are localized in both space and time but display oscillatory behavior, either temporally or spatially, and they often serve as prototypes for nonlinear modulations and the generation of rogue waves. In this study, we consider a generalized wave propagation equation known as generalized Longitudinal Lugiato Lefever equation (gLLLE) which is capable of modeling both passive and active cavities, as well as hybrid structures such as semiconductor ring lasers subject to external optical driving. By employing suitable transformation techniques, we construct a variety of nonlinear excitations, including lump, lump–one strip (LoS), lump–two strip (LtS), lump–periodic (LP), and rogue wave solutions, together with several interaction patterns involving lumps, periodic waves, and kink waves. Moreover, we compute several families of breather solutions, such as Ma breathers (MBs), Kuznetsov-Ma breathers (KMBs), generalized breathers (GBs), and Akhmediev breathers (ABs), together with their associated rogue waves, and depict their structures using 3D, 2D, and contour plots. The outcomes of this study carry strong practical relevance, as lump and breather dynamics underpin applications in optical communication, all-optical switching, ultra-fast pulse generation, and secure information transfer. Furthermore, understanding their interactions sheds light on controlling extreme optical events like rogue waves, which is crucial for the stability of high-power laser systems and fiber-optic networks. Overall, our results offer new insights into the interplay of localized and periodic wave structures, paving the way for advances in integrated photonics, nonlinear optical systems, and next-generation telecommunication technologies.