The first-integral method and abundant explicit exact solutions to the Zakharov equations
type: Item
instance of: scholarly article
title: The first-integral method and abundant explicit exact solutions to the Zakharov equations
zbMATH Open document ID: 1308.65179
DOI: 10.1155/2012/818345
author: Yadong Shang
author: Xiaoxiao Zheng
published in: Journal of Applied Mathematics
publication date: 2013-06-03T00:00:00Z
review text: Summary: This paper is concerned with the system of Zakharov equations which involves the interactions between Langmuir and ion-acoustic waves in plasma. Abundant explicit and exact solutions of the system of Zakharov equations are derived uniformly by using the first integral method. These exact solutions are include that of the solitary wave solutions of bell-type for \(n\) and \(E\), the solitary wave solutions of kink-type for \(E\) and bell-type for \(n\), the singular traveling wave solutions, periodic wave solutions of triangle functions, Jacobi elliptic function doubly periodic solutions, and Weierstrass elliptic function doubly periodic wave solutions. The results obtained confirm that the first integral method is an efficient technique for analytic treatment of a wide variety of nonlinear systems of partial differential equations.
Mathematics Subject Classification ID: 65M99
Mathematics Subject Classification ID: 35Q53
zbMATH DE Number: 6169984
Wikidata QID: Q58907419
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/818345
OpenAlex ID: W2080191471
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description: scientific article; zbMATH DE number 6169984