Symmetries of partial differential equations: conservation laws, applications, algorithms

Description

Content: I (Acta Appl. Math. 15, 1-210).- Symmetries and Conservation Laws of Partial Differential Equations: Basic Notions and Results.- Symmetries and Conservation Laws of Kadomtsev-Pogutse Equations (Their computation and first applications).- Symmetries and Conservation Laws of Navier-Stokes Equations.- Symmetries, Invariant Solutions and Conservation Laws of the Nonlinear Acoustics Equation.- Local Nonintegrability of Long-Short Wave Interaction Equations.- On Symmetries and Conservation Laws of the Equations of Shallow Water with an Axisymmetric Profile of Bottom.- On Symmetries of the Heat Equation.- Nonlocal Trends in the Geometry of Differential Equations: Symmetries, Conservation Laws, and Backlund Transformations.- II (Acta Appl Math. 16, 1-142).- Exactly and Completely Integrable Nonlinear Dynamical Systems.- Recursion and Group Structures of Soliton Equations.- Building of Mathematical Models of Continuum Media on the Basis of the Invariance Principle.- III (Acta Appl. Math. 16,143-242).- Efficiently Implementing Two Methods of the Geometrical Theory of Differential Equations: An Experience in Algorithm and Software Design.- Computations in Differential and Difference Modules.- Reducing Systems of Linear Differential Equations to a Passive Form.- Software to Compute Infinitesimal Symmetries of Exterior Differential Systems, with Applications.- Lie Algebra Computations.