Related papers: Deformations of differential equations
Differential equation discovery, a machine learning subfield, is used to develop interpretable models, particularly in nature-related applications. By expertly incorporating the general parametric form of the equation of motion and…
It is outlined how deformations of field theoretical rigid symmetries can be constructed and classified by cohomological means in the extended antifield formalism. Special attention is devoted to deformations referring only to a subset of…
In this paper we use the deformation procedure introduced in former work on deformed defects to investigate several new models for real scalar field. We introduce an interesting deformation function, from which we obtain two distinct…
Differential systems with a Fuchsian linear part are studied in regions including all the singularities in the complex plane of these equations. Such systems are not necessarily analytically equivalent to their linear part (they are not…
We construct a sequence that converges to a solution of the Cauchy problem for a singularly perturbed linear inhomogeneous differential equation of an arbitrary order. This sequence is also an asymptotic sequence in the following sense: the…
Asymptotic properties of solutions of odd-order nonlinear dispersion equations are studied. The global in time similarity solutions, which lead to eigenfunctions of the rescaled ODEs, are constructed.
We study the effects of adding a local perturbation in a pattern forming system, taking as an example the Ginzburg-Landau equation with a small localized inhomogeneity in two dimensions. Measuring the response through the linearization at a…
We study the evolution of cosmological perturbations, using a hybrid approximation scheme which upgrades the weak-field limit of Einstein's field equations to account for post-Newtonian scalar and vector metric perturbations and for…
The problem of deforming geometries is particularly important in the context of constructing new exact solutions of Einstein's equation. This issue often appears when extensions of the general relativity are treated, for instance in brane…
We review investigations on defects in systems described by real scalar fields in (D,1) space-time dimensions. We first work in one spatial dimension, with models described by one and two real scalar fields, and in higher dimensions. We…
We present some results regarding metric perturbations in general relativity and other metric theories of gravity. In particular, using the Newman Penrose variables, we write down and discuss the equations which govern tensor field…
We connect the discrete and continuous Bogomolny equations. There exists one-parameter algebra relating two equations which is the deformation of the extended conformal algebra. This shows that the deformed algebra plays the role of the…
This paper develops an explicit spectral representation for solutions of a one-dimensional linear wave equation with a constant time delay. The model is considered on a bounded interval with non-homogeneous Dirichlet boundary data and a…
We study non-linear differential equations on the punctured formal disc by considering the natural derived enhancements of their spaces of solutions. In particular, by appealing to results of the inverse theory in the calculus of…
Some properties and relations satisfied by the polynomial solutions of a bispectral problem are studied. Given a finite order differential operator, under certain restrictions, its polynomial eigenfunctions are explicitly obtained, as well…
We consider variational problems that model the bending behavior of curves that are constrained to belong to given hypersurfaces. Finite element discretizations of corresponding functionals are justified rigorously via Gamma-convergence.…
Differential equations with constant and variable coefficients over octonions are investigated. It is found that different types of differential equations over octonions can be resolved. For this purpose non-commutative line integration is…
We discuss a relation between deformed cohomologies of symmetry pseudo-groups and coverings of differential equations. Examples include the potential Khokhlov--Zabolotskaya equation and the Boyer--Finley equation.
We study a class of elliptic problems, involving a $k$-Hessian and a very fast-growing nonlinearity, on a unit ball. We prove the existence of a radial singular solution and obtain its exact asymptotic behavior in a neighborhood of the…
Variational and divergence symmetries are studied in this paper for linear equations of maximal symmetry in canonical form, and the associated first integrals are given in explicit form. All the main results obtained are formulated as…