{"title":"The exploding solitons of the sine–Gordon equation","authors":"Shuzhi Liu , Deqin Qiu","doi":"10.1016/j.aml.2024.109314","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, the hodograph equivalent short pulse (HESP) equations are investigated via the Darboux transformation, we derive the soliton and positon solutions from the “seed” solutions, and then, the decomposition of the lower-order positons into single-solitons is given analytically when time <span><math><mi>T</mi></math></span> is sufficiently large. As a notable new result, we obtain the exploding soliton and positon solutions of the sine–Gordon (SG) equation from the hodograph equivalent short pulse equations.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"160 ","pages":"Article 109314"},"PeriodicalIF":2.9000,"publicationDate":"2024-09-19","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/S0893965924003343","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
In this paper, the hodograph equivalent short pulse (HESP) equations are investigated via the Darboux transformation, we derive the soliton and positon solutions from the “seed” solutions, and then, the decomposition of the lower-order positons into single-solitons is given analytically when time is sufficiently large. As a notable new result, we obtain the exploding soliton and positon solutions of the sine–Gordon (SG) equation from the hodograph equivalent short pulse equations.
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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