Related papers: Integrating the Jacobian equation
We describe the first term of the $\Lambda_{k-1}\mathcal{C}$--spectral sequence (see math.DG/0610917) of the diffiety (E,C), E being the infinite prolongation of an l-normal system of partial differential equations, and C the Cartan…
We look at the decomposition of the compactified jacobian of a singular curve into components and discuss some examples.
We consider the discrete Boussinesq integrable system and the compatible set of differential difference, and partial differential equations. The latter not only encode the complete hierarchy of the Boussisesq equation, but also incorporate…
The Riccati equations reducible to first-order linear equations by an appropriate change the dependent variable are singled out. All these equations are integrable by quadrature. A wide class of linear ordinary differential equations…
The quantum dynamical systems of identical particles admitting an additional integral quadratic in momenta are considered. It is found that an appropriate ordering procedure exists which allows to convert the classical integrals into their…
Our main result describes the relation between the syzygies involving the first order partial derivatives $f_0,...,f_n$ of a homogeneous polynomial $f\in \C[x_0,...x_n]$ and the defect of the linear systems vanishing on the singular locus…
The paper develops the method for construction of families of particular solutions to some classes of nonlinear Partial Differential Equations (PDE). Method is based on the specific link between algebraic matrix equations and PDE.…
The relations between solutions of the three types of totally linear partial differential equations of first order are presented. The approach is based on factorization of a non-homogeneous first order differential operator to products…
This paper intends to construct discrete spectral transformations for Cauchy-Jacobi orthogonal polynomials, and find its corresponding discrete integrable systems. It turns out that the normalization factor of Cauchy-Jacobi orthogonal…
We discuss the inequalities for $q$-integrals because of the fact that the inequalities can be very useful in the future mathematical research. Since $q$-integral of a function over an interval $[a,b]$ is defined by the difference of two…
This work validates and extends the method of integration by differentiation, initially introduced by A. Kempf et al., and demonstrates its compatibility with classical rules of integration. It provides applications to classical integrals,…
A quantum integrable model is considered which describes a quantization of affine hyper-elliptic Jacobian. This model is shown to possess the property of duality: a dual model with inverse Planck constant exists such that the…
Let K[x,y] be the algebra of two-variable polynomials over a field K. A polynomial p=p(x, y) is called a test polynomial (for automorphisms) if, whenever \phi(p)=p for a mapping \phi of K[x,y], this \phi must be an automorphism. Here we…
We show that quadratic Hamiltonians in involution coming from a St\"ackel system are quantizable, in the sense that one can construct commutative self-adjoint operators whose symbols are the quadratic Hamiltonians. Moreover, they allow…
Found all equivalence classes for electromagnetic potentials and space-time metrics of Stackel spaces, provided that the equations of motion of the classical charged test particles are integrated by the method of complete separation of…
In the present paper fractional Hamilton-Jacobi equation has been derived for dynamical systems involving Caputo derivative. Fractional Poisson-bracket is introduced. Further Hamilton's canonical equations are formulated and quantum wave…
Let $F:\Cn \to \Cn$ be a polynomial mapping in Yagzhev's form,i.e. $$F(x_1,\ld,x_n)=(x_1+H_1(x_1,\ld,x_n),\ld,x_n+H_n(x_1,\ld,x_n)),$$ where $H_i$ are homogenous polynomials of degree 3. In this paper we show that if $\Jac(F) \in…
The concepts of differentiation and integration for matrices are known. As far as each matrix is differentiable, it is not clear a priori whether a given matrix is integrable or not. Recently some progress was obtained for diagonalizable…
It is well-known that if a symplectic integrator is applied to a Hamiltonian system, then the modified equation, whose solutions interpolate the numerical solutions, is again Hamiltonian. We investigate this property from the variational…
In this paper we present a two-component generalization of the C-integrable Calogero equation (see [1]). This system is C-integrable as well, and moreover we show that the Calogero equation and its two-component generalization are solvable…