作者：(美)丹尼尔·J.阿里戈(Daniel
页数：180页
出版社：哈尔滨工业大学出版社
出版日期：2024
ISBN：9787576708820
电子书格式：pdf/epub/txt
内容简介
本书是一本获得非线性偏微分方程(NLPDEs)精确解的介绍性书籍。本书包含了非线性PDEs无处不在、相容性、微分替换、点变换与接触变换、第一积分、泛函可分性、解等内容。
目录
PrefaceAcknowledgments1 Nonlinear PDEs are Everywhere1.1 Exercises1.2 References2 Compatibility2.1 Charpit’s Method2.2 Second-Order PDEs2.3 Compatibility in (2 1) Dimensions2.4 Compatibility for Systems of PDEs2.5 Exercises2.6 References3 Differential Substitutions3.1 Generalized Burgers’ Equation3.2 KdV-MKdV Connection3.3 Generalized KdV Equation3.4 Matrix Hopf-Cole Transformation3.5 Darboux Transformations3.5.1 Second-Order Darboux Transformations3.5.2 Darboux Transformations Between Two Diffusion Equations3.5.3 Darboux Transformations Between Two Wave Equations3.6 Exercises3.7 References4 Point and Contact Transformations4.1 Contact Transformations4.1.1 Hodograph Transformation4.1.2 Legendre Transformation4.1.3 Ampere Transformation4.2 Contact Condition4.3 Plateau Problem4.3.1 Linearization4.3.2 Well-known Minimal Surfaces4.4 Exercises4.5 References5 First Integrals5.1 Quasilinear Second-Order Equations5.2 Monge-Ampere Equation5.3 The Martin Equation5.4 First Integrals and Linearization5.4.1 Hyperbolic MA Equations5.4.2 Parabolic MA Equations.5.4.3 Elliptic MA Equations5.5 Exercises5.6 References6 Functional Separability6.1 Exercises6.2 References7 SolutionsAuthor’s Biography编辑手记
