{"title":"Limit solutions of loop solitons for a compound WKI-SP equation","authors":"Gaizhu Qu , Junyang Zhang , Xiaorui Hu , Shoufeng Shen","doi":"10.1016/j.aml.2024.109452","DOIUrl":null,"url":null,"abstract":"<div><div>We characterize the limit solutions of loop solitons for an integrable compound equation which is a mix of the Wadati-Konno-Ichikawa (WKI) equation and the short-pulse (SP) equation. We do so by taking an ingenious limit on the <span><math><mi>τ</mi></math></span>-function derived from Hirota’s bilinear equations of the mKdV-SG (modified Korteweg–de Vries and sine-Gordon) equation. By virtue of a hodograph transformation, we compute the limit solution of 2-loop (noted as <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn><mo>−</mo><mi>l</mi><mi>o</mi><mi>o</mi><mi>p</mi></mrow></msub></math></span>) soliton and discuss the interactions between two <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn><mo>−</mo><mi>l</mi><mi>o</mi><mi>o</mi><mi>p</mi></mrow></msub></math></span> solitons in detail. One singlevalued and two nonsinglevalued limit solutions of 2-breather solution are presented at last.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109452"},"PeriodicalIF":2.9000,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0893965924004725","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
We characterize the limit solutions of loop solitons for an integrable compound equation which is a mix of the Wadati-Konno-Ichikawa (WKI) equation and the short-pulse (SP) equation. We do so by taking an ingenious limit on the -function derived from Hirota’s bilinear equations of the mKdV-SG (modified Korteweg–de Vries and sine-Gordon) equation. By virtue of a hodograph transformation, we compute the limit solution of 2-loop (noted as ) soliton and discuss the interactions between two solitons in detail. One singlevalued and two nonsinglevalued limit solutions of 2-breather solution are presented at last.
期刊介绍：
The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.
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