Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2013, Article ID 142027, 8 pages
http://dx.doi.org/10.1155/2013/142027
Research Article

Exact Solutions for ( )-Dimensional Potential-YTSF Equation and Discrete Kadomtsev-Petviashvili Equation

1Department of Mathematics, Shanghai University, Shanghai 200444, China
2Department of Mathematics, Luoyang Normal University, Luoyang 471022, China
3School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454003, China

Received 4 July 2013; Revised 28 October 2013; Accepted 11 November 2013

Academic Editor: Nazim Idrisoglu Mahmudov

Copyright © 2013 Yan Wang and Zhenhui Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

By employing Hirota bilinear method, we mainly discuss the ( )-dimensional potential-YTSF equation and discrete KP equation. For the former, we use the linear superposition principle to get its exponential wave solutions. In virtue of some Riemann theta function formulas, we also construct its quasiperiodic solutions and analyze the asymptotic properties of these solutions. For the latter, by using certain variable transformations and identities of the theta functions, we explicitly investigate its periodic waves solutions in terms of one-theta function and two-theta functions.