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This is an accessible book on advanced symmetry methods for partial differential equations. Topics include conservation laws, local symmetries, higher-order symmetries, contact transformations, delete "adjoint symmetries," Noether’s theorem, local mappings, nonlocally related PDE systems, potential symmetries, nonlocal symmetries, nonlocal conservation laws, nonlocal mappings, and the nonclassical method. Graduate students and researchers in mathematics, physics, and engineering will find this book useful. This book is a sequel to Symmetry and Integration Methods for Differential Equations (2002) by George W. Bluman and Stephen C. Anco. The emphasis in the present book is on how to find systematically symmetries (local and nonlocal) and conservation laws (local and nonlocal) of a given PDE system and how to use systematically symmetries and conservation laws for related applications.

Differential equations -- Numerical solutions. --- Differential equations, Partial -- Numerical solutions. --- Symmetry (Physics). --- Differential equations, Partial --- Differential equations --- Symmetry (Physics) --- Mathematics --- Algebra --- Calculus --- Mathematical Theory --- Physical Sciences & Mathematics --- Numerical solutions --- Numerical solutions. --- Invariance principles (Physics) --- Symmetry (Chemistry) --- 517.91 Differential equations --- Mathematics. --- Topological groups. --- Lie groups. --- Mathematical analysis. --- Analysis (Mathematics). --- Topological Groups, Lie Groups. --- Analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Groups, Topological --- Continuous groups --- Math --- Science --- Conservation laws (Physics) --- Physics --- Numerical analysis --- Topological Groups. --- Global analysis (Mathematics). --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic

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Nonlinear partial differential equations (PDE) are at the core of mathematical modeling. In the past decades and recent years, multiple analytical methods to study various aspects of the mathematical structure of nonlinear PDEs have been developed. Those aspects include C- and S-integrability, Lagrangian and Hamiltonian formulations, equivalence transformations, local and nonlocal symmetries, conservation laws, and more. Modern computational approaches and symbolic software can be employed to systematically derive and use such properties, and where possible, construct exact and approximate solutions of nonlinear equations. This book contains a consistent overview of multiple properties of nonlinear PDEs, their relations, computation algorithms, and a uniformly presented set of examples of application of these methods to specific PDEs. Examples include both well known nonlinear PDEs and less famous systems that arise in the context of shallow water waves and far beyond. The book will be of interest to researchers and graduate students in applied mathematics, physics, and engineering, and can be used as a basis for research, study, reference, and applications.

Differential equations, Nonlinear. --- Geography --- Mathematics. --- Dynamical systems. --- Biomathematics. --- Mathematics of Planet Earth. --- Dynamical Systems. --- Mathematical and Computational Biology. --- Equacions diferencials no lineals --- Equacions en derivades parcials --- Onades --- Models matemàtics --- Dynamics.