{"title":"N-periodic wave solutions of the (2+1)-dimensional integrable nonlocal nonlinear Schrödinger equations","authors":"Zhonglong Zhao, Yu Wang","doi":"10.1016/j.wavemoti.2025.103526","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, the quasi-periodic wave solutions for the (2+1)-dimensional integrable nonlocal nonlinear Schrödinger equations based on parity-time <span><math><mrow><mo>(</mo><mi>P</mi><mi>T</mi><mo>)</mo></mrow></math></span> symmetry are investigated through numerical algorithm for the first time. By using the Hirota’s bilinear method and the Riemann-theta function, the system of equations for constructing quasi-periodic wave solutions can be viewed as a nonlinear over-determined system. This system can be transformed into a nonlinear least square problem and solved with the aid of the Gauss–Newton algorithm. The asymptotic property of the one-periodic wave under the small amplitude limit is investigated. Furthermore, the dynamical behaviors of the quasi-periodic waves are analyzed by means of the characteristic lines. The method for constructing the quasi-periodic wave solutions can be further extended into other nonlocal integrable equations.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"136 ","pages":"Article 103526"},"PeriodicalIF":2.1000,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Wave Motion","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S016521252500037X","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ACOUSTICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, the quasi-periodic wave solutions for the (2+1)-dimensional integrable nonlocal nonlinear Schrödinger equations based on parity-time symmetry are investigated through numerical algorithm for the first time. By using the Hirota’s bilinear method and the Riemann-theta function, the system of equations for constructing quasi-periodic wave solutions can be viewed as a nonlinear over-determined system. This system can be transformed into a nonlinear least square problem and solved with the aid of the Gauss–Newton algorithm. The asymptotic property of the one-periodic wave under the small amplitude limit is investigated. Furthermore, the dynamical behaviors of the quasi-periodic waves are analyzed by means of the characteristic lines. The method for constructing the quasi-periodic wave solutions can be further extended into other nonlocal integrable equations.
期刊介绍：
Wave Motion is devoted to the cross fertilization of ideas, and to stimulating interaction between workers in various research areas in which wave propagation phenomena play a dominant role. The description and analysis of wave propagation phenomena provides a unifying thread connecting diverse areas of engineering and the physical sciences such as acoustics, optics, geophysics, seismology, electromagnetic theory, solid and fluid mechanics.
The journal publishes papers on analytical, numerical and experimental methods. Papers that address fundamentally new topics in wave phenomena or develop wave propagation methods for solving direct and inverse problems are of interest to the journal.
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