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<p>In this paper, the classification and conversion mechanism of the quasi-periodic breathers for (2+1)-dimensional Schrödinger equation are investigated. The rich evolutionary laws of state transitions and degradation for the quasi-periodic breathers are systematically revealed. The solvable problem for the quasi-periodic breathers can be reorganized into a least squares problem, which can be solved with the help of the generalized Levenberg-Marquardt algorithm and the Riemann-theta function. Various kinds of high-precision numerical approximations of quasi-periodic breathers are obtained. In terms of analytical analysis, it is found that the asymptotic relationship between quasi-periodic breathers and breathers. By means of an analytical method related to the characteristic lines, the dynamical characteristics of quasi-periodic breathers are studied. The mechanism of state transition for the breathers is successfully migrated to the quasi-periodic breathers depending on the ratio of wave numbers. Furthermore, it is illustrated that the degeneration of the quasi-periodic breather into a rogue wave under the specific parametric limit. The results and methodologies provide a further framework applicable to other integrable systems with breathers.</p>

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Quasi-periodic breathers to the \((2+1)\)-dimensional nonlinear Schrödinger equation: conversion mechanism, numerical calculation and classification

  • 期刊论文

  • 发表日期：

    2026年7月23日

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  • Yu Wang,
  • Zhonglong Zhao,
  • Lihan Zhang,
  • Zhaohua Li

摘要

In this paper, the classification and conversion mechanism of the quasi-periodic breathers for (2+1)-dimensional Schrödinger equation are investigated. The rich evolutionary laws of state transitions and degradation for the quasi-periodic breathers are systematically revealed. The solvable problem for the quasi-periodic breathers can be reorganized into a least squares problem, which can be solved with the help of the generalized Levenberg-Marquardt algorithm and the Riemann-theta function. Various kinds of high-precision numerical approximations of quasi-periodic breathers are obtained. In terms of analytical analysis, it is found that the asymptotic relationship between quasi-periodic breathers and breathers. By means of an analytical method related to the characteristic lines, the dynamical characteristics of quasi-periodic breathers are studied. The mechanism of state transition for the breathers is successfully migrated to the quasi-periodic breathers depending on the ratio of wave numbers. Furthermore, it is illustrated that the degeneration of the quasi-periodic breather into a rogue wave under the specific parametric limit. The results and methodologies provide a further framework applicable to other integrable systems with breathers.