Advances in Nonlinear Complexity Analysis for Partial Differential Equations

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.