Related papers: Classification of discrete equations linearizable …

A nonlinear partial differential equation is a nonlinear relationship between an unknown function and how it changes due to two or more input variables. A numerical method reduces such an equation to arithmetic for quick visualization, but…

Some particular examples of classical and quantum systems on the lattice are solved with the help of orthogonal polynomials and its connection to continuous models are explored.

We give some sufficient conditions that ensure oscillations and nonoscillations for nonautonomous impulsive differential equations with piecewise constant arguments of generalized type. We cover several cases of differential equations with…

Recently, it has been great interest in the development of methods for solving nonlinear differential equations directly. Here, it is shown an algorithm based on Pad\'e approximants for solving nonlinear partial differential equations…

We demonstrate that the complete factorization of equations of motion into first-order differential equations can be obtained for real and complex scalar field theories with non-canonical dynamics.

We extend two of the methods previously introduced to find discrete symmetries of differential equations to the case of difference and differential-difference equations. As an example of the application of the methods, we construct the…

We discuss the linearization of a non-autonomous nonlinear partial difference equation belonging to the Boll classification of quad-graph equations consistent around the cube. We show that its Lax pair is fake. We present its generalized…

We construct a sheaf theoretic and derived geometric machinery to study nonlinear partial differential equations and their singular supports. We establish a notion of derived microlocalization for solution spaces of non-linear equations and…

We derive sharp decay estimates and prove holomorphic extensions for the solutions of a class of semilinear nonlocal elliptic equations with linear part given by a sum of Fourier multipliers with finitely smooth symbols at the origin.…

We are concerned with the solvability of linear second order elliptic partial differential equations with nonlinear boundary conditions at resonance, in which the nonlinear boundary conditions perturbation is not necessarily required to…

We obtain existence and multiplicity results for quasilinear fourth order elliptic equations on $\mathbb{R}^{N}$ with sign-changing potential. Our results generalize some recent results on this problem.

In this article we discuss the solvability of some class of fully nonlinear equations, and equations with p-Laplacian in more general conditions by using a new approach given in [1] for studying the nonlinear continuous operator. Moreover…

Point transformations of the 3-rd order ordinary differential equations are considered. Special classes of ordinary differential equations that are invariant under the general point transformations are constructed.

Using the symmetry approach, we find a class of integrable nonlinear PDEs with dispersion law $\omega(k)=k^{\frac32}$. All these equations turn out to be linearizable by means of a differential parametrization.

We classify stable and finite Morse index solutions to general semilinear elliptic equations posed in Euclidean space of dimension at most 10, or in some unbounded domains.

We consider the problem of performing the preliminary "symmetry classification'' of a class of quasi-linear PDE's containing one or more arbitrary functions: we provide an easy condition involving these functions in order that nontrivial…

For a linear differential equation with a mild condition on its singularities, we discuss generalized continued fractions converging to expressions in its solutions and their derivatives. In the case of an order two linear differential…

We consider a new class of quaternionic mappings, associated with the spatial partial differential equations. We describe all mappings from this class using four analytic functions of the complex variable.

Miura-type transformations (MTs) are an essential tool in the theory of integrable nonlinear partial differential and difference equations. We present a geometric method to construct MTs for differential-difference (lattice) equations from…

In this article we present some integrability conditions for partial difference equations obtained using the formal symmetries approach. We apply them to find integrable partial difference equations contained in a class of equations…