求解非線性偏微分方程的分析方法

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編輯手記