Related papers: Lie symmetries and singularity analysis for genera…
A classification of ordinary differential equations and finite-difference equations in one variable having polynomial solutions (the generalized Bochner problem) is given. The method used is based on the spectral problem for a polynomial…
We carry out an extended symmetry analysis of the multi-layer quasi-geostrophic problem. This model is given by a system of an arbitrary number of coupled barotropic vorticity equations. Conservation laws and a Hamiltonian structure for the…
It is well known that the validity of the so called Lenard-Magri scheme of integrability of a bi-Hamiltonian PDE can be established if one has some precise information on the corresponding 1st variational Poisson cohomology for one of the…
The so-called covariant Poincare lemma on the induced cohomology of the spacetime exterior derivative in the cohomology of the gauge part of the BRST differential is extended to cover the case of arbitrary, non reductive Lie algebras. As a…
We perform a detailed Lie symmetry analysis for the hyperbolic system of partial differential equations that describe the one-dimensional Shallow Water magnetohydrodynamics equations within a rotating reference frame. We consider a relaxing…
This paper is devoted to a study of the connections between three different analytic descriptions for the immersion functions of 2D-surfaces corresponding to the following three types of symmetries: gauge symmetries of the linear spectral…
In this paper we consider a generalized Kuramoto-Sivashinsky equation. The equivalence group of the class under consideration has been constructed. This group allows us to perform a comprehensive study and a clear and concise formulation of…
We consider a class of third order equations from the point of view of strict self-adjointness. Necessary and sufficient conditions to the investigated class be strictly self-adjoint are obtained. Then, from a strictly self-adjoint subclass…
We exhaustively classify the Lie reductions of the real dispersionless Nizhnik equation to partial differential equations in two independent variables and to ordinary differential equations. Lie and point symmetries of reduced equations are…
The characterization of systems of differential equations admitting a superposition function allowing us to write the general solution in terms of any fundamental set of particular solutions is discussed. These systems are shown to be…
This paper uses Lie symmetry analysis to investigate the biharmonic heat equation on a generalized surface of revolution. We classify the Lie point symmetries associated with this equation, allowing for the identification of surfaces and…
This paper is a survey article on bi-Hamiltonian systems on the dual of the Lie algebra of vector fields on the circle. We investigate the special case where one of the structures is the canonical Lie-Poisson structure and the second one is…
In this paper we use the symmetry reduction method to obtain invariant solutions of the ideal magnetohydrodynamic equations in (3+1) dimensions. These equations are invariant under a Galilean-similitude Lie algebra for which the…
Based on the Lie symmetry method, we investigate a Feynman-Kac formula for the classical geometric mean reversion process, which effectively describing the dynamics of short-term interest rates. The Lie algebra of infinitesimal symmetries…
In this paper, we consider the steadiness of symmetric solutions to two dispersive models in shallow water and hyperelastic mechanics, respectively. These models are derived previously in the two-dimensional setting and can be viewed as the…
The two-dimensional shallow water equations with a particular bottom and the Coriolis's force $f=f_{0}+\Omega y$ are studied in this paper. The main goal of the paper is to describe all invariant solutions for which the reduced system is a…
Lie symmetry group method is applied to study the Born-Infeld equation. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are obtained. Finally the structure of the Lie algebra…
The Camassa-Holm shallow water equation is known to be Hamiltonian with respect to two compatible Poisson brackets. A set of conjugate variables is constructed for both brackets using spectral theory.
This work presents a classical Lie point symmetry analysis of a two-component, non-isospectral Lax pair of a hierarchy of partial differential equations in $2+1$ dimensions, which can be considered as a modified version of the Camassa-Holm…
The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations…