相关论文: Linearisable third order ordinary differential equ…
This article complements recent results of the papers [J. Math. Phys. 41 (2000), 480; 45 (2004), 336] on the symmetry classification of second-order ordinary difference equations and meshes, as well as the Lagrangian formalism and…
This paper is centred on solving differential equations by symmetry groups for first order ODEs and is in response to Starrett (2007). It also explores the possibility of averting the assumptions by Olver (2000) that, in practice finding…
Line integration of generalized functions is studied. Second order partial differential equations with piecewise continuous and generalized variable coefficients over Cayley-Dickson algebras are investigated. Formulas for integrations of…
A unified treatment is given of low-weight modular forms on \Gamma_0(N), N=2,3,4, that have Eisenstein series representations. For each N, certain weight-1 forms are shown to satisfy a coupled system of nonlinear differential equations,…
We introduce an generalization of the theta divisor to the theory of holomorphic triples on a smooth projective curve $X$. We show that a given triple $T=(E_1 \to E_0)$ is $\alpha$-semistable iff there exists an orthogonal tripe $S=(F_1 \to…
The Universal Field Equations, recently constructed as examples of higher dimensional dynamical systems which admit an infinity of inequivalent Lagrangians are shown to be linearised by a Legendre transformation. This establishes the…
The principle of finding an integrating factor for a none exact differential equations is extended to a class of third order differential equations. If the third order equation is not exact, under certain conditions, an integrating factor…
We consider the third order differential equation derived from the deformed Seiberg-Witten differential for pure ${\cal N}=2$ SYM with gauge group $SU(3)$ in Nekrasov-Shatashvili limit of $\Omega$-background. We show that this is the same…
Coupled second order nonlinear differential equations are of fundamental importance in dynamics. In this part of our study on the integrability and linearization of nonlinear ordinary differential equations we focus our attention on the…
In this paper we give necessary and sufficient conditions for a bounded linear operator $T$ to be generalized Drazin-Riesz invertible or generalized Drazin-meromorphic invertible. Also, we study generalized Browder's theorem and generalized…
Identifying integrable coupled nonlinear ordinary differential equations (ODEs) of dissipative type and deducing their general solutions are some of the challenging tasks in nonlinear dynamics. In this paper we undertake these problems and…
First order algebraic differential equations are considered. An necessary condition for a first order algebraic differential equation to have a rational general solution is given: the algebraic genus of the equation should be zero.…
In this paper, we prove the partial linearization for n-dimensional nonautonomous differential equations. The conditions are formulated in terms of the dichotomy spectrum.
We report a new analytical method for solution of a wide class of second-order differential equations with eigenvalues replaced by arbitrary functions. Such classes of problems occur frequently in Quantum Mechanics and Optics. This approach…
We give an example of infinite order rational transformation that leaves a linear differential equation covariant. This example can be seen as a non-trivial but still simple illustration of an exact representation of the renormalization…
Nonlinear PDE's having {\bf given} conditional symmetries are constructed. They are obtained starting from the invariants of the "conditional symmetry" generator and imposing the extra condition given by the characteristic of the symmetry.…
We generalize results of Rosenlicht to give a necessary and sufficient condition for when order one differential equations of the form $D(x) = f(x)$ where $f$ is a rational function is orthogonal to the constants. Following the main results…
This research is concerned with the nonhomogeneous linear complex differential equation $$ f^{(k)}+A_{k-1}f^{(k-1)}+\cdots+A_{1}f'+A_{0}f=A_{k} $$ in the complex plane. In the higher order case, the mutual relations between coefficients and…
We solve an inverse problem for a third order differential operator under the 3-point Dirichlet conditions. The third-order operator is an $L$-operator in the Lax pair for the good Boussinesq equation. We construct the mapping from the set…
We present the exact solution to the non linear Monge differential equation lambda(x, t)lambdax(x, t) = lambdat(x, t). It is widely accepted that the Monge equation is equivalent to the ODE d2X/dt2= 0 of free motion for particular…