{"title":"Derivation of weakly interacting lumps for the (2+1)-dimensional Yu–Toda–Sasa–Fukuyama equation via degeneracy of lump chains","authors":"Xinru Guo, Wentao Li, Biao Li","doi":"10.1016/j.wavemoti.2024.103423","DOIUrl":null,"url":null,"abstract":"<div><div>This paper introduces two distinct pathways for degenerating normally interacting lump chains into weakly interacting lump waves for Yu–Toda–Sasa–Fukuyama equation, which will enrich the correlation between lump chains and weakly interacting lump waves. The first pathway involves letting the periods of <span><math><mi>M</mi></math></span> similarly-velocity lump chains approach infinity directly. The second pathway first transforms <span><math><mi>M</mi></math></span> normally interacting lump chains into weakly interacting lump chains with similar dynamic behaviors. Then, by allowing their periods to approach infinity, <span><math><mfrac><mrow><mi>M</mi><mfenced><mrow><mi>M</mi><mo>+</mo><mn>1</mn></mrow></mfenced></mrow><mrow><mn>2</mn></mrow></mfrac></math></span> weakly interacting lump waves are produced. Distance between weakly interacting lump chains in this equation is proportional to <span><math><mrow><mo>ln</mo><mo>|</mo><mi>t</mi><mo>|</mo></mrow></math></span>, while between weakly interacting lump waves is proportional to <span><math><mroot><mrow><mo>|</mo><mi>t</mi><mo>|</mo></mrow><mrow><mn>3</mn></mrow></mroot></math></span>. These findings will contribute valuable theoretical insights to the study of wave theory, ocean science and related disciplines.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"132 ","pages":"Article 103423"},"PeriodicalIF":2.1000,"publicationDate":"2024-10-22","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/S0165212524001537","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
This paper introduces two distinct pathways for degenerating normally interacting lump chains into weakly interacting lump waves for Yu–Toda–Sasa–Fukuyama equation, which will enrich the correlation between lump chains and weakly interacting lump waves. The first pathway involves letting the periods of similarly-velocity lump chains approach infinity directly. The second pathway first transforms normally interacting lump chains into weakly interacting lump chains with similar dynamic behaviors. Then, by allowing their periods to approach infinity, weakly interacting lump waves are produced. Distance between weakly interacting lump chains in this equation is proportional to , while between weakly interacting lump waves is proportional to . These findings will contribute valuable theoretical insights to the study of wave theory, ocean science and related disciplines.
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.