2.6 Invertible Mappings of Nonlinear PDEs to Linear PDEs Through Conservation Law Multipliers
2.6.1 Computational steps
2.6.2 Examples of linearizations of nonlinear PDEs through conservation law multipliers
2.7 Discussion

3 Nonlocally Related PDE Systems
3.1 Introduction
3.2 Nonlocally Related Potential Systems and Subsystems in Two Dimensions
3.2.1 Potential systems
3.2.2 Nonlocally related subsystems
3.3 Trees of Nonlocally Related PDE Systems
3.3.1 Basic procedure of tree construction
3.3.2 A tree for a nonlinear diffusion equation
3.3.3 A tree for planar gas dynamics（PGD）equations
3.4 Nonlocal Conservation Laws
3.4.1 Conservation laws arising from nonlocally related systems
3.4.2 Nonlocal conservation laws for diffusion-convection equations
3.4.3 Additional conservation laws of nonlinear telegraph equations
3.5 Extended Tree Construction Procedure
3.5.1 An extended tree construction procedure
3.5.2 An extended tree for a nonlinear diffusion equation
3.5.3 An extended tree for a nonlinear wave equation
3.5.4 An extended tree for the planar gas dynamics equations
3.6 Discussion

4 Applications of Nonlocally Related PDE Systems
4.1 Introduction
4.2 Nonlocal Symmetries
4.2.1 Nonlocal symmetries of a nonlinear diffusion equation
4.2.2 NonlocAL symmetries of a nonlinear wave equation
4.2.3 Classification of nonlocal symmetries of nonlinear telegraph equations arising from point symmetries of potential systems
4.2.4 Nonlocal symmetries of nonlinear telegraph equations with power law nonlinearities
4.2.5 Nonlocal symmetries of the planar gas dynamics equations
4.3 Construction of Non-invertible Mappings Relating PDEs
4.3.1 Non-invertible mappings of nonlinear PDE systems to linear PDE systems
4.3.2 Non-invertible mappings of linear PDEs with variable coefficients to linear PDEs with constant coefficients.
4.4 Discussion

5 Further Applications of Symmetry Methods： Miscellaneous Extensions
5.1 Introduction
5.2 Applications of Symmetry Methods to the Construction of Solutions of PDEs
5.2.1 The classical method
5.2.2 The nonclassical method
5.2.3 Invariant solutions arising from nonlocal symmetries that are local symmetries of nonlocally related systems
5.2.4 Futrther extensions of symmetry methods for construction of solutions of PDEs connected with nonlocaUy related systems
5.3 Nonlocally Related PDE Systems in Three or More Dimensions
5.3.1 Divergence-type conservation laws and resulting potential systems
5.3.2 Nonlocally related subsystems
5.3.3 Tree construction，nonlocal conservation laws，and nonlocal symmetries
5.3.4 Lower-degree conservation laws and related potential systems
5.3.5 Examples of applications of nonlocally related systems in higher dimensions
5.3.6 Symmetries and exact solutions of the three-dimensional MHD equilibrium equations
5.4 Symbolic Software
5.4.1 An example of symbolic computation of point symmetries
5.4.2 An example of point symmetry classification
5.4.3 An example of symbolic computation of conservation laws
5.5 Discussion
References
Theorem，Corollary and Lemma Index
Author Index
Subject Index

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