Intermediate systems and invariants
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O. V. Kaptsov
Abstract
In this paper some classical and new methods of integration of partial differential equations are considered. The approaches of Monge and Darboux are briefly described. Examples of the construction of general solutions of second-order equations based on invariants of the characteristics of hyperbolic equations are given. Intermediate systems of partial derivative equations are introduced in terms of differential algebra. Equations possessing intermediate systems are found.
Abstract
In this paper some classical and new methods of integration of partial differential equations are considered. The approaches of Monge and Darboux are briefly described. Examples of the construction of general solutions of second-order equations based on invariants of the characteristics of hyperbolic equations are given. Intermediate systems of partial derivative equations are introduced in terms of differential algebra. Equations possessing intermediate systems are found.
Chapters in this book
- Frontmatter I
- Preface V
- Contents VII
- About the editors IX
- List of contributors XI
- Intermediate systems and invariants 1
- Folding in fluids 19
- Vortex models of plane turbulent flows 37
- Equations of dyon electromagnetic field 53
- Minimal action principle for gravity and electrodynamics, Einstein lambda, and Lagrange points 65
- Methods for constructing invariant conservative finite-difference schemes for hydrodynamic-type equations 83
- On exact analytical solutions of equations of Maxwell incompressible viscoelastic medium 111
- Approximate solution of a boundary-value problem for a model of the far momentumless turbulent wake 125
- Analysis of overdetermined system that describes the special class of two-dimensional motion of an ideal fluid 135
- Discrete orthogonal polynomials: anomalies of time series and boundary effects of polynomial filters 143
- Index 165
Chapters in this book
- Frontmatter I
- Preface V
- Contents VII
- About the editors IX
- List of contributors XI
- Intermediate systems and invariants 1
- Folding in fluids 19
- Vortex models of plane turbulent flows 37
- Equations of dyon electromagnetic field 53
- Minimal action principle for gravity and electrodynamics, Einstein lambda, and Lagrange points 65
- Methods for constructing invariant conservative finite-difference schemes for hydrodynamic-type equations 83
- On exact analytical solutions of equations of Maxwell incompressible viscoelastic medium 111
- Approximate solution of a boundary-value problem for a model of the far momentumless turbulent wake 125
- Analysis of overdetermined system that describes the special class of two-dimensional motion of an ideal fluid 135
- Discrete orthogonal polynomials: anomalies of time series and boundary effects of polynomial filters 143
- Index 165
