Abstract and Applied Analysis

Volume 2013 (2013), Article ID 585716, 1 page

http://dx.doi.org/10.1155/2013/585716

Editorial

Advances in Nonlinear Complexity Analysis for Partial Differential Equations

Zhengde Dai,¹ Qianshun S. Chang,² Lan Xu,³ Syed Tauseef Mohyud-Din,⁴ Hafez Tari,⁵ and Peicheng Zhu⁶

¹School of Mathematics and Statistics, Yunnan University, Kunming 650091, China

²Institute of Applied Mathematics and System Sciences, Academy of Sciences of China, Beijing 100080, China

³National Engineering Laboratory for Modern Silk, Soochow University, Suzhou 215123, China

⁴Department of Mathematics, HITEC University, Taxila Cantt, Pakistan

⁵Department of Mechanical Engineering, Ohio State University, Columbus, OH 43210, USA

⁶Department of Mathematics, University of the Basque Country (UPV/EHU) and IKERBASQUE, Basque Foundation for Science, 48011 Bilbao, Spain

Received 19 August 2013; Accepted 19 August 2013

Copyright © 2013 Zhengde Dai et al. 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.

Nonlinear Partial Differential Equations (NPDE) including integrable, nearintegrable, and nonintegrable systems arise from a number of physical, chemical, biological, and life sciences. The complexity analysis of solutions for NPDE is a very important subject in nonlinear science all the time. In recent years, this research field has taken many new advances. The purpose of this special issue is to highlight some recent researches carried out on the asymptotical behavior analysis of solution with initial boundary value problem, spatiotemporal feature analysis, variety analysis of dynamics, stochastic behavior analysis, numerical simulation and analysis, and so forth.

We have received 81 submissions to the special issue which were rigorously reviewed by up to 8 reviewers as well as by at least one of the guest editors; all the manuscripts had 2 reviewers. As a result, 27 manuscripts are accepted. In these articles, the most new results in the research field of nonlinear complexity of solutions are obtained. We hope that this special issue can lead to both theoretical insight and practical applications in nonlinear complexity analysis for NPDE.

Acknowledgments

We would like to thank the authors of all the contributions, the reviewers for their useful and timely comments on the papers submitted to this issue.

Zhengde Dai

Qianshun S. Chang

Lan Xu

Syed Tauseef Mohyud-Din

Hafez Tari

Peicheng Zhu