[PDF] Top 20 Second order integrability conditions for difference equations. An integrable equation.

... an equation admits a second order formal recursion operator but does not satisfy the first order integrability conditions, then the square root of the recursion operator cannot ... See full document

... The analytic solution is constructed on the basis of the incomplete separation of variables and of reduction to a problem for a second- order functional difference-equation (SOFDE). Though the latter ... See full document

... of second order differential equations [1] [2] difference equ- ations of the type (E) and/or related equations have been investigated by many authors, for example see, [3]-[19] and the ... See full document

... By lemma 2   u n 0 for all n sufficiently large so that { } u n is non-decreasing; it then follows from conditions (i)-(iii) that there is positive constant  such that   f g n u ( ( ), g n ( ) ) for all n ... See full document

... establish conditions for the existence of periodic solutions of nonlinear, second-order difference equations of the form y(t + 2) + by(t + 1) + cy(t) = f (y(t)), where c = 0 and f : R → R is ... See full document

... difference equations became a popular topic for ...crete equations, the spectral theory of quantum difference equations has been treated in the last decade ... See full document

... for second-order di ff erence ...of second-order difference equation with three di ff erent coupled boundary conditions are ... See full document

... delay difference equations, that is, difference equations in which the highest order difference of the unknown sequence appears both with and without delays, have considerable ... See full document

... above equation is transformed into a new one, which is a third-order non-neutral difference ...new equation, the asymptotic properties of the neutral difference equation are ...sufficient ... See full document

... cient conditions so that all its solutions be directionally oscillatory, as well as conditions which guarantee the existence of directionally positive monotone increasing ... See full document

... Definition 1.3. By a solution of (1.6) we mean a function u : { a,a + 1,... ,b + 1,b + 2 } → R which satisfies the difference equation and the boundary value conditions in (1.6). Theorem 1.4. Let h : T → R ... See full document

... When δ = 1, equation (1) has been considered in [17] and [19]. When δ = 1 and ∇ F(n, x) = 0, equation (1) has been also studied. For example, in [1] and [8], the authors were interested in the results on ... See full document

... equations and the Banach fixed point theorem we present some sufficient conditions for the existence of a unique bounded solution to equation (). In the third section we will present another way for ... See full document

... differential equations serve as basic models to study the dynamics of processes that are subject to sudden changes in their ...differential equations, we refer the interested reader to the monographs ... See full document

... [1] V. A. Ilin and E. I. Moiseev, Nonlocal boundary-value problem of the first kind for a Sturm-Liouville operator in its differential and finite difference aspects, J. Differential Equations 23(1987), ... See full document

... initial conditions and to introduce a small parameter ...of integrable discrete systems 13, 14, it turned out that the confinement property was not sufficient in order to guarantee integrability ... See full document

... q-difference equations. For instance, our results correspond to the ones for second-order q-difference equations with anti-periodic boundary conditions (u(0) = -u (T), D q ... See full document

... Another main instrument to handle the time-fractional derivative is the L formula. Sun and Wu [] first proposed a fully discrete difference scheme for FSDE by employing the L approximation, where the truncation error ... See full document

... Obviously, gravitation pulls things downward toward the center of the Earth. If you were on another planet, you would find gravitation there, too, but it would not pull on you with the same amount of force. If you weigh ... See full document

... wave equations. The nonlinear Schrödinger equation is one of the most fundamental modes admitting RWs ...Schrödinger-type equations have been reported to have rogue wave solutions ...Schrödinger ... See full document