Results 1 to 10 of about 1,118 (52)

On integrable conservation laws. [PDF]

Proc Math Phys Eng Sci, 2015
We study normal forms of scalar integrable dispersive (non necessarily Hamiltonian) conservation laws via the Dubrovin-Zhang perturbative scheme. Our computations support the conjecture that such normal forms are parametrised by infinitely many arbitrary
Arsie A, Lorenzoni P, Moro A.
europepmc   +4 more sources

Computer Algebra Solving of Second Order ODEs Using Symmetry Methods [PDF]

, 1998
An update of the ODEtools Maple package, for the analytical solving of 1st and 2nd order ODEs using Lie group symmetry methods, is presented. The set of routines includes an ODE-solver and user-level commands realizing most of the relevant steps of the ...
Bluman, Cheb-Terrab, Cheb-Terrab, E.S. Cheb-Terrab, Gonzáles López, González-López, Hereman, L.A.C.P. da Mota, L.G.S. Duarte, Olver, Olver, Reid, Reid, Stephani, Zwillinger   +14 more
core   +3 more sources

On integrability of (2+1)-dimensional quasilinear systems [PDF]

, 2003
A (2+1)-dimensional quasilinear system is said to be `integrable' if it can be decoupled in infinitely many ways into a pair of compatible n-component one-dimensional systems in Riemann invariants.
Boyer, Burnat, Burnat, Burnat, Canic, Dinu, Dubrovin, E.V. Ferapontov, Ferapontov, Ferapontov, Gibbons, Gibbons, Gibbons, Gibbons, Godunov, Grundland, Hereman, Hietarinta, K.R. Khusnutdinova, Krichever, Krichever, Manas, Mikhailov, Peradzyński, Peradzyński, Tsarev   +25 more
core   +6 more sources

Dispersionless integrable systems in 3D and Einstein-Weyl geometry [PDF]

, 2013
For several classes of second order dispersionless PDEs, we show that the symbols of their formal linearizations define conformal structures which must be Einstein-Weyl in 3D (or self-dual in 4D) if and only if the PDE is integrable by the method of ...
Ferapontov, Eugene, Kruglikov, Boris
core   +2 more sources

Compatibility, multi-brackets and integrability of systems of PDEs [PDF]

, 2008
We establish an efficient compatibility criterion for a system of generalized complete intersection type in terms of certain multi-brackets of differential operators.
Kruglikov, Boris, Lychagin, Valentin
core   +2 more sources

Integrable viscous conservation laws [PDF]

, 2014
We propose an extension of the Dubrovin-Zhang perturbative approach to the study of normal forms for non-Hamiltonian integrable scalar conservation laws. The explicit computation of the first few corrections leads to the conjecture that such normal forms
Arsie, Alessandro, Lorenzoni, Paolo, Moro, Antonio   +2 more
core   +2 more sources

Riemann Invariants and Rank-k Solutions of Hyperbolic Systems [PDF]

, 2005
In this paper we employ a "direct method" in order to obtain rank-k solutions of any hyperbolic system of first order quasilinear differential equations in many dimensions.
Burnat M, Courant R, Dafermos C, Doyle P W, Dubrovin B A, Ferapontov E V, Ferapontov E V, Ferapontov E V, Grundland A M, Grundland A M, Grundland A M, John F, Majda A, Olver P J, Olver P J, Pavlov M V, Peradzynski Z, Peradzynski Z, Poisson S D, Rozdestvenskii B   +19 more
core   +3 more sources

Scalar differential invariants of symplectic Monge–Ampère equations [PDF]

, 2011
All second order scalar differential invariants of symplectic hyperbolic and elliptic Monge-Ampère PDEs with respect to symplectomorphisms are explicitly computed. In particular, it is shown that the number of independent second order invariants is equal
A. M. Vinogradov, DE PARIS, ALESSANDRO
core   +1 more source

A Lie symmetry analysis and explicit solutions of the two-dimensional ∞-Polylaplacian [PDF]

, 2018
In this work, we consider the Lie point symmetry analysis of a strongly nonlinear partial differential equation of third order, the ∞‐Polylaplacian, in two spatial dimensions.
Ablowitz, Aronsson, Ayanbayev, Baikov, Barron, Barron, Bhattacharya, Bluman, Bluman, Clarkson, Conte, Cox, Dimas, Dimas, Elmoataz, Evans, Fordy, Freire, Gyulov, Hereman, Hydon, Ibragimov, Igbida, Jensen, Katzourakis, Katzourakis, Katzourakis, Lazer, Oliveri, Olver, Ovsiannikov, Patera, Pryer, Reid, Schwarz, Stephani, Winternitz, Winternitz, Yaglom, Šnobl   +39 more
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On a class of three-dimensional integrable Lagrangians [PDF]

, 2004
We characterize non-degenerate Lagrangians of the form $ \int f(u_x, u_y, u_t) dx dy dt $ such that the corresponding Euler-Lagrange equations $ (f_{u_x})_x+ (f_{u_y})_y+ (f_{u_t})_t=0 $ are integrable by the method of hydrodynamic reductions.
Ferapontov, E. V., Khusnutdinova, K. R., Tsarev, S. P.   +2 more
core   +3 more sources