Results 1 to 10 of about 2,195,394 (132)

On the geometry of lambda-symmetries, and PDEs reduction [PDF]

J. Phys. A 37 (2004), 6955-6975, 2004
We give a geometrical characterization of $\lambda$-prolongations of vector fields, and hence of $\lambda$-symmetries of ODEs. This allows an extension to the case of PDEs and systems of PDEs; in this context the central object is a horizontal one-form $\mu$, and we speak of $\mu$-prolongations of vector fields and $\mu$-symmetries of PDEs.
arxiv   +1 more source

Solvable Nonlinear Evolution PDEs in Multidimensional Space [PDF]

SIGMA 2 (2006), 088, 17 pages, 2006
A class of solvable (systems of) nonlinear evolution PDEs in multidimensional space is discussed. We focus on a rotation-invariant system of PDEs of Schr\"odinger type and on a relativistically-invariant system of PDEs of Klein-Gordon type. Isochronous variants of these evolution PDEs are also considered.
arxiv   +1 more source

Poisson vertex algebras and Hamiltonian PDE [PDF]

arXiv, 2023
We discuss the theory of Poisson vertex algebras and their generalizations in relation to integrability of Hamiltonian PDE. In particular, we discuss the theory of affine classical W-algebras and apply it to construct a large class of integrable Hamiltonian PDE.
arxiv  

On integration of multidimensional version of $n$-wave type equation [PDF]

Journal of Mathematical Physics, v.55, 121505 (2014), 2014
We represent a version of multidimensional quasilinear partial differential equation (PDE) together with large manifold of particular solutions given in an integral form. The dimensionality of constructed PDE can be arbitrary. We call it the $n$-wave type PDE, although the structure of its nonlinearity differs from that of the classical completely ...
arxiv   +1 more source

Explicit solutions of PDE via Vessiot theory and solvable structures [PDF]

, 2014
We consider the problem of computing the integrable sub-distributions of the non-integrable Vessiot distribution of multi-dimensional second order partial differential equations (PDEs). We use Vessiot theory and solvable structures to find the largest integrable distributions contained in the Vessiot distribution associated to second order PDEs.
arxiv   +1 more source

A Symbolic Algorithm for Computing Recursion Operators of Nonlinear PDEs [PDF]

International Journal of Computer Mathematics, vol. 87(5), pp. 1094-119 (2010), 2009
A recursion operator is an integro-differential operator which maps a generalized symmetry of a nonlinear PDE to a new symmetry. Therefore, the existence of a recursion operator guarantees that the PDE has infinitely many higher-order symmetries, which is a key feature of complete integrability.
arxiv   +1 more source

The decomposition method and Maple procedure for finding first integrals of nonlinear PDEs of any order with any number of independent variables [PDF]

arXiv, 2007
In present paper we propose seemingly new method for finding solutions of some types of nonlinear PDEs in closed form. The method is based on decomposition of nonlinear operators on sequence of operators of lower orders. It is shown that decomposition process can be done by iterative procedure(s), each step of which is reduced to solution of some ...
arxiv  

Quantum extended crystal PDE's [PDF]

Nonlinear Studies 18(3)(2011), 1-39, 2011
Our recent results on {\em extended crystal PDE's} are generalized to PDE's in the category $\mathfrak{Q}_S$ of quantum supermanifolds. Then obstructions to the existence of global quantum smooth solutions for such equations are obtained, by using algebraic topologic techniques.
arxiv  

Odd-Symplectic group in First order PDE [PDF]

Int. Jou. of Pure and Applied Mathematics 2003 Vol. 6 N. 2, pages 203-216, 2002
It is shown that the characteristic vector field associated to a first order PDE has the same form of an infinitesimal generator of an odd-symplectic transformation with contact Hamiltonian the given PDE. It is considered under which condition such PDE has a characteristic vector field commuting with a generator of an odd-symplectic action.
arxiv  

Nonlinear PDEs risen when solving some optimization problems in finance, and their solutions [PDF]

arXiv, 2015
We consider a specific type of nonlinear partial differential equations (PDE) that appear in mathematical finance as the result of solving some optimization problems. We review some existing in the literature examples of such problems, and discuss the properties of these PDEs.
arxiv