期刊
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
卷 371, 期 2, 页码 585-608出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2010.05.070
关键词
Hirota bilinear method; Riemann theta function; Periodic wave solution; Solitary wave solution; The Caudrey-Dodd-Gibbon-Sawada-Kotera equation; The (2+1)-dimensional breaking soliton equation
资金
- National Key Basic Research Project of China [2004CB318000]
- Natural Sciences Foundation of China [50909017]
- Dalian University of Technology
In this paper, based on a multidimensional Riemann theta function, a lucid and straightforward generalization of the Hirota-Riemann method is presented to explicitly construct multiperiodic Riemann theta functions periodic wave solutions for nonlinear equations such as the Caudrey-Dodd-Gibbon-Sawada-Kotera equation and (2 + 1)-dimensional breaking soliton equation. Among these periodic waves, the one-periodic waves are well-known cnoidal waves, their surface pattern is one-dimensional, and often they are used as one-dimensional models of periodic waves. The two-periodic waves are a direct generalization of one-periodic waves, their surface pattern is two-dimensional so that they have two independent spatial periods in two independent horizontal directions. A limiting procedure is presented to analyze in detail, asymptotic behavior of the multiperiodic waves and the relations between the periodic wave solutions and soliton solutions are rigorously established. This generalized Hirota-Riemann method can also be demonstrated on a class variety of nonlinear difference equations such as Toeplitz lattice equation. (C) 2010 Elsevier Inc. All rights reserved.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据