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2012 The First-Integral Method and Abundant Explicit Exact Solutions to the Zakharov Equations
Yadong Shang, Xiaoxiao Zheng
J. Appl. Math. 2012: 1-16 (2012). DOI: 10.1155/2012/818345

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.

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Yadong Shang. Xiaoxiao Zheng. "The First-Integral Method and Abundant Explicit Exact Solutions to the Zakharov Equations." J. Appl. Math. 2012 1 - 16, 2012. https://doi.org/10.1155/2012/818345

Information

Published: 2012
First available in Project Euclid: 2 January 2013

zbMATH: 1308.65179
MathSciNet: MR2991598
Digital Object Identifier: 10.1155/2012/818345

Rights: Copyright © 2012 Hindawi

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