The book introduces the existence, uniqueness, regularity and the long time behavior of solutions with respect to space and time, and the explosion phenomenon for some evolution equations, including the KdV equation, the nonlinear Schrödinger equation, the sine-Gordon equation, the Zakharov equations, the Landau-Lifshitz equations, the Boussinesq equation, the Navier-Stokes equations and the Newton-Boussinesq equations etc., as well as the basic concepts and research methods of infinite-dimensional dynamical systems. This book presents fundamental elements and important advances in nonlinear evolution equations. It is intended for senior university students, graduate students, postdoctoral fellows and young teachers to acquire a basic understanding of this field, while providing a reference for experienced researchers and teachers in natural sciences and engineering technology to broaden their knowledge.

Contributor: Boling GUO

Guo Boling, an academician of Chinese Academy of Sciences, a renowned expert in applied mathematics and computational mathematics, research fellow of Institute of Applied Physics and Computational Mathematics, has made great achievements in qualitative and numerical study on the solutions, soliton solutions of nonlinear evolution equations, as well as infinite-dimensional dynamical systems. In addition to over 700 essays published on important journals home and abroad, he is the author of over ten books and 15 volumes of essays. He is the winner of the first prize and the third prize of National Natural Science Award, Guanghua Engineering Science and Technology Award, the Ho Leung Ho Lee (HLHL) Foundation Award, etc.

Fei CHEN (Associate Professor, School of Mathematics and Statistics, Qingdao University) focuses on research into well-posedness and large-time behavior to solutions of some fluid mechanics equations.

Jing SHAO (Associate Professor, Normal College, Shenyang University) carries out research on qualitative theory of fractional differential equations.

Ting LUO (Assistant professor, Master Advisor, School of Mathematical Sciences, Zhejiang Normal University) has her main research interest on stability theory of nonlinear wave equations, water waves, modeling and analysis of simplified phenomenological models, and integrable system.