{"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}
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.
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.
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