editorial advances in nonlinear complexity analysis for...

Hindawi Publishing Corporation Abstract and Applied Analysis Volume 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 Zhu 6 1 School of Mathematics and Statistics, Yunnan University, Kunming 650091, China 2 Institute of Applied Mathematics and System Sciences, Academy of Sciences of China, Beijing 100080, China 3 National Engineering Laboratory for Modern Silk, Soochow University, Suzhou 215123, China 4 Department of Mathematics, HITEC University, Taxila Cantt, Pakistan 5 Department of Mechanical Engineering, Ohio State University, Columbus, OH 43210, USA 6 Department of Mathematics, University of the Basque Country (UPV/EHU) and IKERBASQUE, Basque Foundation for Science, 48011 Bilbao, Spain Correspondence should be addressed to Zhengde Dai; [email protected] Received 19 August 2013; Accepted 19 August 2013 Copyright © 2013 Zhengde Dai et al. is 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. e 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. e 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

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Page 1: Editorial Advances in Nonlinear Complexity Analysis for ...downloads.hindawi.com/journals/aaa/2013/585716.pdf · Advances in Nonlinear Complexity Analysis for Partial Differential

Hindawi Publishing CorporationAbstract and Applied AnalysisVolume 2013, Article ID 585716, 1 pagehttp://dx.doi.org/10.1155/2013/585716

EditorialAdvances in Nonlinear Complexity Analysis for PartialDifferential Equations

Zhengde Dai,1 Qianshun S. Chang,2 Lan Xu,3 Syed Tauseef Mohyud-Din,4

Hafez Tari,5 and Peicheng Zhu6

1 School of Mathematics and Statistics, Yunnan University, Kunming 650091, China2 Institute of Applied Mathematics and System Sciences, Academy of Sciences of China, Beijing 100080, China3National Engineering Laboratory for Modern Silk, Soochow University, Suzhou 215123, China4Department of Mathematics, HITEC University, Taxila Cantt, Pakistan5 Department of Mechanical Engineering, Ohio State University, Columbus, OH 43210, USA6Department of Mathematics, University of the Basque Country (UPV/EHU) and IKERBASQUE, Basque Foundation for Science,48011 Bilbao, Spain

Correspondence should be addressed to Zhengde Dai; [email protected]

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) includingintegrable, nearintegrable, and nonintegrable systems arisefrom a number of physical, chemical, biological, and lifesciences. The complexity analysis of solutions for NPDE isa very important subject in nonlinear science all the time.In recent years, this research field has taken many newadvances. The purpose of this special issue is to highlightsome recent researches carried out on the asymptoticalbehavior analysis of solution with initial boundary valueproblem, spatiotemporal feature analysis, variety analysis ofdynamics, stochastic behavior analysis, numerical simulationand analysis, and so forth.

We have received 81 submissions to the special issuewhich were rigorously reviewed by up to 8 reviewers as wellas by at least one of the guest editors; all the manuscriptshad 2 reviewers. As a result, 27 manuscripts are accepted.In these articles, the most new results in the research fieldof nonlinear complexity of solutions are obtained. We hopethat this special issue can lead to both theoretical insight andpractical applications in nonlinear complexity analysis forNPDE.

Acknowledgments

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

Zhengde DaiQianshun S. Chang

Lan XuSyed Tauseef Mohyud-Din

Hafez TariPeicheng Zhu