Related papers: A new recursion operator for the Viallet equation
We consider second order uniformly elliptic operators of divergence form in $\R^{d+1}$ whose coefficients are independent of one variable. For such a class of operators we establish a factorization into a product of first order operators…
Differential equations on spaces of operators are very little developed in Mathematics, being in general very challenging. Here, we study a novel system of such (non-linear) differential equations. We show it has a unique solution for all…
Moving frames of various kinds are used to derive bi-Hamiltonian operators and associated hierarchies of multi-component soliton equations from group-invariant flows of non-stretching curves in constant curvature manifolds and Lie group…
We prove the existence of classical solutions to the Dirichlet problem for a class of fully nonlinear elliptic equations of curvature type on Riemannian manifolds. We also derive new second derivative boundary estimates which allows us to…
The paper is a presentation of recent investigations on potential scattering in R^3. We advocate a new formula for the wave operators and deduce the various outcomes that follow from this formula. A topological version of Levinson's theorem…
A time operator is a Hermitian operator that is canonically conjugate to a given Hamiltonian. For a particle in 1-dimension, a Hamiltonian conjugate operator in position representation can be obtained by solving a hyperbolic second-order…
A computer-algebra aided method is carried out, for determining geometric objects associated to differential operators that satisfy the elliptic ansatz. This results in examples of Lame curves with double reduction and in the explicit…
We analyze and compare the methods of construction of the recursion operators for a special class of integrable nonlinear differential equations related to A.III-type symmetric spaces in Cartan's classification and having additional…
We examine the multiple Hamiltonian structure and construct a symplectic realization of the Volterra model. We rediscover the hierarchy of invariants, Poisson brackets and master symmetries via the use of a recursion operator. The rational…
The existence theory is developed for solutions of the inhomogeneous linearized field equations for causal variational principles. These equations are formulated weakly with an integral operator which is shown to be bounded and symmetric on…
We propose new vertex operators, both the type I and the type II dual, of the elliptic quantum toroidal algebra U_{t_1,t_2,p}(gl_{1,tor}) by combining representations of U_{t_1,t_2,p}(gl_{1,tor}) and the notions of the elliptic stable…
We consider one-dimensional inhomogeneous parabolic equations with higher-order elliptic differential operators subject to periodic boundary conditions. In our main result we show that the property of continuous maximal regularity is…
A novel formulation of the Lie-Darboux method of obtaining the Riccati equations for the spatial curves in Euclidean three-dimensional space is presented. It leads to two Riccati equations that differ by the sign of torsion. The case of…
In this short note, we solve a Dirichlet problem for a fully nonlinear elliptic equation. The operator is introduced by S. Donaldson and it is relevant to the geometry of the space of volume forms.
We give a general method for constructing recursion operators for some equations of hydrodynamic type, admitting a nonstandard Lax representation. We give several examples for N=2 and N=3 containing the equations of shallow water waves and…
An explicit formula to find symmetry recursion operators for partial differential equations (PDEs) is obtained from new results connecting variational integrating factors and non-variational symmetries. The formula is special case of a…
We proposed an algorithm that covers some cases of Hamilton Circuit Problem.
We first strictly expressed the basic notions and research methods of abstract operators, which systematically expounded the main results of abstract operator theory. By combining abstract operators with the Laplace transform, we can easily…
New elliptic cylindrical wavelets are introduced, which exploit the relationship between analysing filters and Floquet's solution of Mathieu differential equations. It is shown that the transfer function of both multiresolution filters is…
In this paper we investigate the existence of nodal solutions to elliptic problem involving the GJMS operators on Riemannian manifold with boundary