scientific article
From MaRDI portal
Publication:3431229
zbMath1122.53044MaRDI QIDQ3431229
Vladimir Rubtsov, Valentin V. Lychagin, Alexei G. Kushner
Publication date: 10 April 2007
Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Symplectic manifolds (general theory) (53D05) Contact manifolds (general theory) (53D10) Exterior differential systems (Cartan theory) (58A15) Research exposition (monographs, survey articles) pertaining to differential geometry (53-02) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02) Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory (37-02) Research exposition (monographs, survey articles) pertaining to ordinary differential equations (34-02) Contact systems (37J55)
Related Items
Attractors in models of porous media flow ⋮ Complete spelling rules for the Monster tower over three-space ⋮ Meta-symplectic geometry of \(3^{\mathrm{rd}}\) order Monge-Ampère equations and their characteristics ⋮ Differential invariants and exact solutions of the Einstein equations ⋮ Symmetries and Integrals ⋮ Finite Dimensional Dynamics of Evolutionary Equations with Maple ⋮ Group classification of Rapoport-Leas equations ⋮ Differential invariants for spherical layer flows of viscid fluids ⋮ Computation of partially invariant solutions for the Einstein Walker manifolds' identifying equations ⋮ Integrable structures for a generalized Monge-Ampère equation ⋮ Finding solutions of parabolic Monge-Ampère equations by using the geometry of sections of the contact distribution ⋮ SYMMETRY ANALYSIS AND SIMILARITY REDUCTION OF THE KORTEWEG–DE VRIES–ZAKHAROV–KUZNETSOV EQUATION ⋮ Automorphisms of symplectic and contact structures ⋮ A general method to construct invariant PDEs on homogeneous manifolds ⋮ Control of displacement front in a model of immiscible two-phase flow in porous media ⋮ Exhaustive Classification of the Invariant Solutions for a Specific Nonlinear Model Describing Near Planar and Marginally Long-Wave Unstable Interfaces for Phase Transition ⋮ Geometry of distributions and \(F\)-Gordon equation ⋮ Some remarks on contact manifolds, Monge–Ampère equations and solution singularities ⋮ On automorphism groups of natural contact structures on a bundle of 1-jet functions ⋮ Petrov invariants of Hamiltonian systems with a control parameter ⋮ Control of a mobile robot with a trailer based on nilpotent approximation ⋮ Invariant manifolds of a weakly dissipative version of the nonlocal Ginzburg-Landau equation ⋮ Thermodynamics as a theory of measurement ⋮ Monge-Ampère equations on (para-)Kähler manifolds: from characteristic subspaces to special Lagrangian submanifolds ⋮ On global solvability of initial value problem for hyperbolic Monge-Ampère equations and systems ⋮ Local bifurcations in the periodic boundary value problem for the generalized Kuramoto-Sivashinsky equation ⋮ Geometry of a quasilinear system of two partial differential equations of the 1st and 2nd order in two functions of two independent variables ⋮ Travelling wave solution of the Buckley-Leverett equation ⋮ Singularities of multivalued solutions of quasilinear hyperbolic systems ⋮ On exact solutions of nonlinear acoustic equations ⋮ Contact geometry of the Pontryagin maximum principle ⋮ Phase transitions in filtration of Redlich-Kwong gases ⋮ Exceptionally simple PDE ⋮ New integrable (\(3+1\))-dimensional systems and contact geometry ⋮ Integration of the deep bed filtration equations ⋮ On quasilinearization of elliptic Monge-Ampère systems ⋮ Geometry of jet spaces and integrable systems ⋮ Symmetry analysis and conservation laws of the geodesic equations for the Reissner-Nordström de Sitter black hole with a global monopole ⋮ TOPOLOGICALLY MASSIVE ABELIAN GAUGE THEORY ⋮ Affine contact manifolds with automorphism group of maximal dimension ⋮ Minkowski metrics on solutions of the Khokhlov-Zabolotskaya equation ⋮ Critical phenomena in filtration processes of real gases ⋮ Contact geometry of multidimensional Monge-Ampère equations: characteristics, intermediate integrals and solutions ⋮ On the geometry of quadratic second-order Abel ordinary differential equations ⋮ Lie symmetry analysis of the two-dimensional generalized Kuramoto-Sivashinsky equation ⋮ Differential geometry and mechanics: a source for computer algebra problems ⋮ Geometric theory of special modes in the distributed-parameter control systems ⋮ Scalar differential invariants of symplectic Monge-Ampère equations ⋮ Dynamics of evolutionary PDE systems ⋮ Geometric study of gas behavior in a one-dimensional nozzle (the case of the van der Waals gas) ⋮ Shock waves in Euler flows of gases ⋮ Solutions of second-order PDEs with first-order quotients ⋮ On global solvability of one-dimensional quasilinear wave equations ⋮ Canonical distributions on Riemannian homogeneous \(k\)-symmetric spaces ⋮ An introduction to completely exceptional second order scalar partial differential equations ⋮ Cartan's structure theory of symmetry pseudo-groups, coverings and multi-valued solutions for the Khokhlov-Zabolotskaya equation ⋮ A contact linearization problem for Monge-Ampère equations and Laplace invariants ⋮ Contact relative differential invariants for non generic parabolic Monge-Ampère equations ⋮ Entropy in thermodynamics: from foliation to categorization ⋮ Differential invariants for spherical flows of a viscid fluid ⋮ Group classification of Buckley-Leverett system ⋮ Contact manifolds, Lagrangian Grassmannians and PDEs ⋮ Differential invariants of feedback transformations for quasi-harmonic oscillation equations ⋮ Completely exceptional 2nd order PDEs via conformal geometry and BGG resolution ⋮ On the global solubility of the Cauchy problem for hyperbolic Monge–Ampére systems ⋮ Lie algebras of conservation laws of variational partial differential equations ⋮ Contact geometry in optimal control of thermodynamic processes for gases ⋮ On differential invariants and classification of ordinary differential equations of the form \(y = A(x, y)y' + B(x, y)\) ⋮ \(r\)-tuple almost product structures ⋮ The Lie group in infinite dimension ⋮ Differential invariants of the 2D conformal Lie algebra action ⋮ Projective structures and algebras of their differential invariants ⋮ Compatible structures on Lie algebroids and Monge-Ampère operators ⋮ On contact equivalence of Monge-Ampère equations to linear equations with constant coefficients ⋮ Comprehensive analysis of the symmetries and conservation laws of the geodesic equations for a particular string inspired FRLW solution ⋮ Schrödinger equations on elliptic curves: symmetries, solutions and eigenvalue problem ⋮ On geometry of second-order parabolic equations in two independent variables ⋮ Transformation of hyperbolic Monge-Ampère equations into linear equations with constant coefficients ⋮ On the integrability of symplectic Monge-Ampère equations ⋮ Computing the Maslov index of solitary waves. II: Phase space with dimension greater than four ⋮ Differential invariants for spherical flows of inviscid fluid ⋮ Singularities in one-dimensional Euler flows ⋮ Differential invariants for spherical layer flows of inviscid fluids ⋮ Real gas flows issued from a source ⋮ Dynamics and exact solutions of non-evolutionary partial differential equations ⋮ Multiple solutions in Euler's elastic problem ⋮ Computing the Maslov index of solitary waves. I: Hamiltonian systems on a four-dimensional phase space ⋮ Geometric Hamiltonian formalism for reparameterization-invariant theories with higher derivatives ⋮ \(\mathbb R\)-conformal invariants of curves ⋮ Contact linearization of nondegenerate Monge-Ampère equations ⋮ Remarks on non-maximal integral elements of the Cartan plane in jet spaces ⋮ Normal forms for Lagrangian distributions on 5-dimensional contact manifolds ⋮ Wei-Norman equations for classical groups via cominuscule induction ⋮ On the inverse variational problem for one class of quasilinear equations ⋮ Exact solutions of the Burgers-Huxley equation via dynamics ⋮ Transformations of Darboux Integrable Systems ⋮ The geometry of a quasilinear system of two partial differential equations containing the first and the second partial derivatives of two functions in two independent variables ⋮ Contact linearization of Monge-Ampère equations and Laplace invariants ⋮ Classification of Lie Subalgebras up to an Inner Automorphism ⋮ Differential invariants and exact solutions of the Einstein-Maxwell equation ⋮ On a class of integrable systems of Monge-Ampère type ⋮ APPLICATION OF CARTAN’S EQUIVALENCE METHOD TO DISTRIBUTION OF PLANES ⋮ Invariant volume forms and first integrals for geodesically equivalent Finsler metrics ⋮ On the quasilinearizability of hyperbolic Monge-Ampère systems ⋮ On a generalization of Monge-Ampère equations and Monge-Ampère systems ⋮ Bi-Hamiltonian structure of a unit geodesic vector field on a 3D space of constant negative curvature ⋮ The aromatic bicomplex for the description of divergence-free aromatic forms and volume-preserving integrators ⋮ From modelling of systems with constraints to generalized geometry and back to numerics ⋮ Evolutionary systems and flows on solutions spaces of finite type equations ⋮ Contact transformations in theory of frontal oil displacement ⋮ The moment map on the space of symplectic 3D Monge-Ampère equations ⋮ Ricci flow on contact manifolds
