相关论文: Perturbative methods for the Painlev\'e test

The well established monotone iterative technique that is used to study the existence and uniqueness of fractional impulsive system is extended to Hilfer fractional order in this paper. The results are derived by using the method of upper…

We study multiplicative SDEs perturbed by an additive fractional Brownian motion on another probability space. Provided the Hurst parameter is chosen in a specified regime, we establish existence of probabilistically weak solutions to the…

Three symbolic algorithms for testing the integrability of polynomial systems of partial differential and differential-difference equations are presented. The first algorithm is the well-known Painlev\'e test, which is applicable to…

The paper concerns the solvability by quadratures of linear differential systems, which is one of the questions of differential Galois theory. We consider systems with regular singular points as well as those with (non-resonant) irregular…

When a solution to the Cauchy problem for nonlinear dispersive equations is obtained by a fixed point argument using auxiliary function spaces, it is non-trivial to ensure uniqueness of solutions in a natural space such as the class of…

We apply Painlev\'e test to the most general variable coefficient nonlinear Schrodinger (VCNLS) equations as an attempt to identify integrable classes and compare our results versus those obtained by the use of other tools like…

In the work we use integral formulas for calculating the monodromy data for the Painlev\'e-2 equation. The perturbation theory for the auxiliary linear system is constructed and formulas for the variation of the monodromy data are obtained.…

We analyze perturbative aspects of gauged matrix models, including those where classically the gauge symmetry is partially broken. Ghost fields play a crucial role in the Feynman rules for these vacua. We use this formalism to elucidate the…

In this study, the existence and uniqueness of the unpredictable solution for a non-homogeneous linear system of ordinary differential equations is considered. The hyperbolic case is under discussion. New properties of unpredictable…

We prove the necessary and sufficient condition for the removability of the fundamental singularity, and equivalently for the unique solvability of the singular Dirichlet problem for the heat equation. In the measure-theoretical context,…

We consider a power-type mild singular perturbation of a Dirichlet semilinear critical problem settled in an open and bounded set in a Carnot group. Here, the term critical has to be understood in the sense of the Sobolev embedding. We aim…

We consider a perturbed system $(X,\varphi(\epsilon,\cdot))$, where $X$ is a topological Markov shift with a countably infinite state space, and $\varphi(\epsilon,\cdot)$ is a real-valued potential on X depending on a small parameter…

The concept of gauge invariance in classical electrodynamics assumes tacitly that Maxwell's equations have unique solutions. By calculating the electromagnetic field of a moving particle both in Lorenz and in Coulomb gauge and directly from…

By defining two important terms called basic perturbation vectors and obtaining their linear bounds, we obtain the linear componentwise perturbation bounds for unitary factors and upper triangular factors of the generalized Schur…

In this paper we first give the explicit definition of essential perturbation. Secondly, given a perturbation of a particular family of centers of polynomial differential systems of arbitrary degree for which we explicitly know its…

The present article investigates the existence, multiplicity and regularity of weak solutions of problems involving a combination of critical Hartree type nonlinearity along with singular and discontinuous nonlinearity. By applying…

Discrete numerical methods with finite time-steps represent a practical technique to solve initial-value problems involving nonlinear differential equations. These methods seem particularly useful to the study of chaos since no analytical…

We present a brief overview of integrability of nonlinear ordinary and partial differential equations with a focus on the Painleve property: an ODE of second order has the Painleve property if the only movable singularities connected to…

A periodic perturbation generates a complicated dynamics close to separatrices and saddle points. We construct an asymptotic solution which is close to the separatrix for the unperturbed Duffing's oscillator over a long time. This solution…

Even if it is nonintegrable, a differential equation may nevertheless admit particular solutions which are globally analytic. On the example of the dynamical system of Kuramoto and Sivashinsky, which is generically chaotic and presents a…