Quasi-Lie schemes for PDEs
DOI10.1142/S0219887819500968zbMath1423.35012arXiv1712.02238OpenAlexW2963074751WikidataQ114072340 ScholiaQ114072340MaRDI QIDQ5233038
Janusz Grabowski, José F. Cariñena, Javier de Lucas
Publication date: 13 September 2019
Published in: International Journal of Geometric Methods in Modern Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1712.02238
Wess-Zumino-Novikov-Witten modelBäcklund transformationAbel differential equationLie systemquasi-Lie schemenonlinear superposition rule
Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Lie algebras of vector fields and related (super) algebras (17B66) Model quantum field theories (81T10) Applications of Lie groups to the sciences; explicit representations (22E70) Groups and algebras in quantum theory and relations with integrable systems (81R12) Geometric theory, characteristics, transformations in context of PDEs (35A30) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)
Related Items
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Geometry of Riccati equations over normed division algebras
- Integrable dissipative nonlinear second order differential equations via factorizations and Abel equations
- A class of exact solutions of the Liénard-type ordinary nonlinear differential equation
- Superposition rules and second-order Riccati equations
- A nonlinear superposition rule for solutions of the Milne-Pinney equation
- The Riccati equation: Initial values and inequalities
- Hamiltonian methods in the theory of solitons. Transl. from the Russian by A. G. Reyman
- Recent applications of the theory of Lie systems in Ermakov systems
- Periodic solutions of Abel differential equations
- Complex parabolic subgroups of \(G_ 2\) and nonlinear differential equations
- Integration of nonlinear equations of mathematical physics by the method of inverse scattering. II
- Abel ODEs: Equivalence and integrable classes
- Riccati-type equations, generalised WZNW equations, and multidimensional Toda systems
- Dirac-Lie systems and Schwarzian equations
- \(k\)-symplectic Lie systems: theory and applications
- On the geometry of the Clairin theory of conditional symmetries for higher-order systems of PDEs with applications
- Quasi-Lie families, schemes, invariants and their applications to Abel equations
- Low dimensional Vessiot-Guldberg-Lie algebras of second-order ordinary differential equations
- Superposition rules, Lie theorem, and partial differential equations
- Soliton surfaces in the generalized symmetry approach
- Integrable Abel equations and Vein's Abel equation
- Solvability of a Lie algebra of vector fields implies their integrability by quadratures
- From constants of motion to superposition rules for Lie–Hamilton systems
- Superposition rules for higher order systems and their applications
- PERIODIC FIRST INTEGRALS FOR HAMILTONIAN SYSTEMS OF LIE TYPE
- Lie systems: theory, generalisations, and applications
- Superposition principles for matrix Riccati equations
- APPLICATIONS OF LIE SYSTEMS IN DISSIPATIVE MILNE–PINNEY EQUATIONS
- Lie–Hamilton systems on the plane: applications and superposition rules
- Lie families: theory and applications
- Quasi-Lie schemes and Emden–Fowler equations
- Quasi-Lie schemes: theory and applications
- Simple subgroups of simple Lie groups and nonlinear differential equations with superposition principles
- Superposition formulas for rectangular matrix Riccati equations
- Integrable Models
- An Abel ordinary differential equation class generalizing known integrable classes
- Poisson–Hopf algebra deformations of Lie–Hamilton systems
- Nonlinear superposition formulas based on imprimitive group action
- Nonlinear equations with superposition formulas and the exceptional group G2. I. Complex and real forms of g2 and their maximal subalgebras
- THREE-DIMENSIONAL DYNAMICAL SYSTEMS WITH FOUR-DIMENSIONAL VESSIOT-GULDBERG-LIE ALGEBRAS
- Yang–Baxter and reflection maps from vector solitons with a boundary
- U(1)-invariant membranes: The geometric formulation, Abel, and pendulum differential equations
- A geometric approach to integrability conditions for Riccati equations
- On Solutions of Certain Riccati Differential Equations
- Lie groups
- The superposition principle for the Lie type first-order PDEs
- Reduction of time-dependent systems admitting a superposition principle
