kdv-nkdv方程的行波

IF 1 4区数学 Q3 MATHEMATICS, APPLIED

Journal of Applied Analysis and Computation Pub Date : 2023-01-01 DOI:10.11948/20230100

Xueqiong Yi, Yuqian Zhou, Qian Liu

{"title":"kdv-nkdv方程的行波","authors":"Xueqiong Yi, Yuqian Zhou, Qian Liu","doi":"10.11948/20230100","DOIUrl":null,"url":null,"abstract":"In this paper, we use the dynamical system method to investigate the wave solutions of the KdV-nKdV equation. We prove Wazwaz’s proposal that the KdV-nKdV equation has continuous periodic wave solutions and give their exact expressions by elliptic integral theory. We confirm that the KdV-nKdV equation has no classical solitary wave solution although it can be regarded as a fusion of the KdV equation with classical solitary wave and the nKdV equation. In addition, we obtain some novel traveling wave solutions of it including trapezoidal wave, inverted ‘N’ wave, and blow-up wave solutions.","PeriodicalId":48811,"journal":{"name":"Journal of Applied Analysis and Computation","volume":"146 1","pages":"0"},"PeriodicalIF":1.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"TRAVELING WAVES OF THE KDV-NKDV EQUATION\",\"authors\":\"Xueqiong Yi, Yuqian Zhou, Qian Liu\",\"doi\":\"10.11948/20230100\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we use the dynamical system method to investigate the wave solutions of the KdV-nKdV equation. We prove Wazwaz’s proposal that the KdV-nKdV equation has continuous periodic wave solutions and give their exact expressions by elliptic integral theory. We confirm that the KdV-nKdV equation has no classical solitary wave solution although it can be regarded as a fusion of the KdV equation with classical solitary wave and the nKdV equation. In addition, we obtain some novel traveling wave solutions of it including trapezoidal wave, inverted ‘N’ wave, and blow-up wave solutions.\",\"PeriodicalId\":48811,\"journal\":{\"name\":\"Journal of Applied Analysis and Computation\",\"volume\":\"146 1\",\"pages\":\"0\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Applied Analysis and Computation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.11948/20230100\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Analysis and Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.11948/20230100","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 1

摘要

本文用动力系统方法研究了KdV-nKdV方程的波动解。用椭圆积分理论证明了Wazwaz关于KdV-nKdV方程具有连续周期波解的建议，并给出了它们的精确表达式。我们证实了KdV-nKdV方程没有经典孤立波解，尽管它可以看作是KdV方程与经典孤立波和nKdV方程的融合。此外，我们还得到了它的一些新的行波解，包括梯形波解、倒“N”波解和爆破波解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

TRAVELING WAVES OF THE KDV-NKDV EQUATION

In this paper, we use the dynamical system method to investigate the wave solutions of the KdV-nKdV equation. We prove Wazwaz’s proposal that the KdV-nKdV equation has continuous periodic wave solutions and give their exact expressions by elliptic integral theory. We confirm that the KdV-nKdV equation has no classical solitary wave solution although it can be regarded as a fusion of the KdV equation with classical solitary wave and the nKdV equation. In addition, we obtain some novel traveling wave solutions of it including trapezoidal wave, inverted ‘N’ wave, and blow-up wave solutions.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Applied Analysis and Computation MATHEMATICS, APPLIED-

CiteScore

2.30

自引率

9.10%

发文量

期刊介绍： The Journal of Applied Analysis and Computation (JAAC) is aimed to publish original research papers and survey articles on the theory, scientific computation and application of nonlinear analysis, differential equations and dynamical systems including interdisciplinary research topics on dynamics of mathematical models arising from major areas of science and engineering. The journal is published quarterly in February, April, June, August, October and December by Shanghai Normal University and Wilmington Scientific Publisher, and issued by Shanghai Normal University.