{"title":"（3 + 1）维Mikhailov-Novikov-Wang方程对称性及新精确解的综合研究","authors":"Ashutosh Kumar Karna, Purnima Satapathy","doi":"10.1007/s10440-025-00744-8","DOIUrl":null,"url":null,"abstract":"<div><p>This article investigates new exact solutions for the (3 + 1)–dimensional Mikhailov-Novikov-Wang equation, an extension of the (1 + 1)–dimensional Mikhailov-Novikov-Wang equation, which is notable for its connection to higher symmetries and the Boussinesq equation, complete integrability. While the Mikhailov-Novikov-Wang equation has been extensively studied and shown to be integrable with multiple soliton solutions, recent research has extended this to higher dimensions. The extended Mikhailov-Novikov-Wang equation has been found to be Painlevé integrable, yielding various soliton solutions such as rational, periodic, and kink-type solitons. Interestingly, while previous literature has primarily focused on soliton solutions, a comprehensive symmetry analysis of the equation remains unexplored to best of our knowledge. Here, we provide thorough exploration of the symmetries of the equation, including both classical and non-classical symmetries. By utilizing these symmetries, we are able to obtain exact solutions and illustrate them graphically, which enhances our comprehension of the dynamics of the equation.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"199 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Comprehensive Study on Symmetry and New Exact Solutions for (3 + 1) – Dimensional Mikhailov-Novikov-Wang Equation\",\"authors\":\"Ashutosh Kumar Karna, Purnima Satapathy\",\"doi\":\"10.1007/s10440-025-00744-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This article investigates new exact solutions for the (3 + 1)–dimensional Mikhailov-Novikov-Wang equation, an extension of the (1 + 1)–dimensional Mikhailov-Novikov-Wang equation, which is notable for its connection to higher symmetries and the Boussinesq equation, complete integrability. While the Mikhailov-Novikov-Wang equation has been extensively studied and shown to be integrable with multiple soliton solutions, recent research has extended this to higher dimensions. The extended Mikhailov-Novikov-Wang equation has been found to be Painlevé integrable, yielding various soliton solutions such as rational, periodic, and kink-type solitons. Interestingly, while previous literature has primarily focused on soliton solutions, a comprehensive symmetry analysis of the equation remains unexplored to best of our knowledge. Here, we provide thorough exploration of the symmetries of the equation, including both classical and non-classical symmetries. By utilizing these symmetries, we are able to obtain exact solutions and illustrate them graphically, which enhances our comprehension of the dynamics of the equation.</p></div>\",\"PeriodicalId\":53132,\"journal\":{\"name\":\"Acta Applicandae Mathematicae\",\"volume\":\"199 1\",\"pages\":\"\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2025-09-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Applicandae Mathematicae\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10440-025-00744-8\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Applicandae Mathematicae","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10440-025-00744-8","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
A Comprehensive Study on Symmetry and New Exact Solutions for (3 + 1) – Dimensional Mikhailov-Novikov-Wang Equation
This article investigates new exact solutions for the (3 + 1)–dimensional Mikhailov-Novikov-Wang equation, an extension of the (1 + 1)–dimensional Mikhailov-Novikov-Wang equation, which is notable for its connection to higher symmetries and the Boussinesq equation, complete integrability. While the Mikhailov-Novikov-Wang equation has been extensively studied and shown to be integrable with multiple soliton solutions, recent research has extended this to higher dimensions. The extended Mikhailov-Novikov-Wang equation has been found to be Painlevé integrable, yielding various soliton solutions such as rational, periodic, and kink-type solitons. Interestingly, while previous literature has primarily focused on soliton solutions, a comprehensive symmetry analysis of the equation remains unexplored to best of our knowledge. Here, we provide thorough exploration of the symmetries of the equation, including both classical and non-classical symmetries. By utilizing these symmetries, we are able to obtain exact solutions and illustrate them graphically, which enhances our comprehension of the dynamics of the equation.
期刊介绍：
Acta Applicandae Mathematicae is devoted to the art and techniques of applying mathematics and the development of new, applicable mathematical methods.
Covering a large spectrum from modeling to qualitative analysis and computational methods, Acta Applicandae Mathematicae contains papers on different aspects of the relationship between theory and applications, ranging from descriptive papers on actual applications meeting contemporary mathematical standards to proofs of new and deep theorems in applied mathematics.
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