Journal of Applied Mathematics

The First-Integral Method and Abundant Explicit Exact Solutions to the Zakharov Equations

Yadong Shang and Xiaoxiao Zheng

Full-text: Open access

Abstract

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.

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 818345, 16 pages.

Dates
First available in Project Euclid: 2 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.jam/1357153566

Digital Object Identifier
doi:10.1155/2012/818345

Mathematical Reviews number (MathSciNet)
MR2991598

Zentralblatt MATH identifier
1308.65179

Citation

Shang, Yadong; Zheng, Xiaoxiao. The First-Integral Method and Abundant Explicit Exact Solutions to the Zakharov Equations. J. Appl. Math. 2012 (2012), Article ID 818345, 16 pages. doi:10.1155/2012/818345. https://projecteuclid.org/euclid.jam/1357153566


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