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<p>In the paper, localized wave and quasi-periodic wave solutions for two types of generalized nonlocal parity-time (PT)-symmetric Davey–Stewartson-type (DS-type) systems are investigated. These systems have potential applications in many fields such as nonlinear optics, plasma physics, and fluid dynamics. The <i>N</i>-soliton solutions are obtained based on the bilinear theory. For the generalized <i>y</i>-nonlocal DS-type system, three types of breathers and their interaction solutions with periodic line waves are derived. By applying long wave limit and partial long wave limit, three types of lumps and the interaction solutions among lump, breather and periodic line waves are obtained. For the generalized <i>xy</i>-nonlocal DS-type system, two types of periodic wave solutions are obtained. Based on long wave limit, the rogue waves are derived from the <i>N</i>-soliton solutions. The interaction solutions between rogue waves and periodic line waves are obtained by adding constraints to the parameters. Combining the bilinear equation with Riemann-theta function, the <i>N</i>-periodic wave solutions are successfully obtained. The difficulty of solving quasi-periodic wave solutions is transformed into solving the least square problem of the nonlinear systems. A generalized Levenberg–Marquardt (LM) algorithm is proposed to solve this kind of problem. Under the influence of nonlocal symmetry in the <i>y</i>-direction, the quasi-periodic waves exhibit a process of splitting and fusion over time <i>t</i>. A series of new solutions, including the quasi-periodic breathers, the quasi-periodic double-peakon breathers, the quasi-periodic double-chain breathers, are acquired. The quasi-periodic waves of the generalized <i>xy</i>-nonlocal DS-type system exhibit similar dynamical behaviors to the ordinary quasi-periodic waves. Their dynamical behaviors are quantitatively analyzed by using the analysis method of the characteristic line. The asymptotic properties of rogue waves, lump waves and quasi-periodic waves are analyzed and explained. These methods can be further broadened to study other complex wave structures for the nonlocal systems.</p>

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Localized Wave and Quasi-Periodic Wave Solutions for the Generalized (2+1)-Dimensional Nonlocal Davey–Stewartson-Type System

  • 期刊论文

  • 发表日期：

    2026年6月30日

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  • Zhonglong Zhao,
  • Yu Wang,
  • Yindi Liu,
  • Shou-Fu Tian

摘要

In the paper, localized wave and quasi-periodic wave solutions for two types of generalized nonlocal parity-time (PT)-symmetric Davey–Stewartson-type (DS-type) systems are investigated. These systems have potential applications in many fields such as nonlinear optics, plasma physics, and fluid dynamics. The N-soliton solutions are obtained based on the bilinear theory. For the generalized y-nonlocal DS-type system, three types of breathers and their interaction solutions with periodic line waves are derived. By applying long wave limit and partial long wave limit, three types of lumps and the interaction solutions among lump, breather and periodic line waves are obtained. For the generalized xy-nonlocal DS-type system, two types of periodic wave solutions are obtained. Based on long wave limit, the rogue waves are derived from the N-soliton solutions. The interaction solutions between rogue waves and periodic line waves are obtained by adding constraints to the parameters. Combining the bilinear equation with Riemann-theta function, the N-periodic wave solutions are successfully obtained. The difficulty of solving quasi-periodic wave solutions is transformed into solving the least square problem of the nonlinear systems. A generalized Levenberg–Marquardt (LM) algorithm is proposed to solve this kind of problem. Under the influence of nonlocal symmetry in the y-direction, the quasi-periodic waves exhibit a process of splitting and fusion over time t. A series of new solutions, including the quasi-periodic breathers, the quasi-periodic double-peakon breathers, the quasi-periodic double-chain breathers, are acquired. The quasi-periodic waves of the generalized xy-nonlocal DS-type system exhibit similar dynamical behaviors to the ordinary quasi-periodic waves. Their dynamical behaviors are quantitatively analyzed by using the analysis method of the characteristic line. The asymptotic properties of rogue waves, lump waves and quasi-periodic waves are analyzed and explained. These methods can be further broadened to study other complex wave structures for the nonlocal systems.