《偏微分方程与孤波理论》讲述了：Partial Differential Equations and Solitary Waves Theory is a self-containedbook divided into two parts: Part I is a coherent survey bringing together newlydeveloped methods for solving PDEs. While some traditional techniques are pre-sented, this part does not require thorough understanding of abstract theories orcompact concepts. Well-selected worked examples and exercises shall guide thereader through the text. Part II provides an extensive exposition of the solitarywaves theory. This part handles nonlinear evolution equations by methods suchas Hirota's bilinear method or the tanh-coth method. A self-contained treatmentis presented to discuss complete integrability of a wide class of nonlinear equa-tions. This part presents in an accessible manner a systematic presentation ofsolitons, multi-soliton solutions, kinks, peakons, cuspons, and compactons. While the whole book can be used as a text for advanced undergraduate andgraduate students in applied mathematics, physics and engineering, Part II willbe most useful for graduate students and researchers in mathematics, engineer-ing, and other related fields.