Related papers: The numerical study of the solution of the $\Phi_0…
Bilinear dynamical systems are ubiquitous in many different domains and they can also be used to approximate more general control-affine systems. This motivates the problem of learning bilinear systems from a single trajectory of the…
In this paper, a new rigorous numerical method to compute fundamental matrix solutions of non-autonomous linear differential equations with periodic coefficients is introduced. Decomposing the fundamental matrix solutions $\Phi(t)$ by their…
We establish sharp global regularity of a class of multilinear oscillatory integral operators that are associated to nonlinear dispersive equations with both Banach and quasi-Banach target spaces. As a consequence we also prove the (local…
In this article, we propose an idea to develop some sufficient conditions for the existence and uniqueness of a positive definite common solution to a pair of non-linear matrix equations. To proceed this, we present some interesting common…
In this paper we consider a system of three fractional differential equations describing a nonlinear reaction. Our analysis includes both analytical technique and numerical simulation. This allows us to control the efficiency of the…
We consider positive solutions to semilinear elliptic problems with singular nonlinearities, under zero Dirichlet boundary condition. We exploit a refined version of the moving plane method to prove symmetry and monotonicity properties of…
In this paper, we develop a systematical approach in applying an asymptotic method of moving planes to investigate qualitative properties of positive solutions for fractional parabolic equations. We first obtain a series of needed key…
The motion of a charged particle moving on a flat surface is studied through the constants of motion associated to the system, given the magnetic gauge. The usual Landau' solution and the non separable solution for the Landau's gauge are…
In this paper a fluid-structure interaction problem for the incompressible Newtonian fluid is studied. We prove the convergence of an iterative process with respect to the computational domain geometry. In our previous works on numerical…
The motive behind this manuscript is to set up the existence and uniqueness of a positive solution for a fractional thermostat model for certain values of the parameter $\lambda>0$. We accomplish sufficient conditions for the existence of a…
In this paper, we introduce an iterative numerical method to solve systems of nonlinear equations. The third-order convergence of this method is analyzed. Several examples are given to illustrate the efficiency of the proposed method.
The solution of the O$(N) \phi^4$ scalar field theory in the broken phase is given in the framework of light cone quantization and a 1/N expansion. It involves the successive building of operator solutions to the equation of motion and…
This paper deals with the stability analysis of a nonlinear time-delayed dispersive equation of order four. First, we prove the well-posedness of the system and give some regularity results. Then, we show that the zero solution of the…
We present a method for solving a class of initial valued, coupled, non-linear differential equations with `moving singularities' subject to some subsidiary conditions. We show that this type of singularities can be adequately treated by…
The non-perturbative autonomous renormalization of the scalar $\Phi^4$-model is applied in the framework of stochastic quantization. I show that this requires a selective, momentum-dependent renormalization of the Onsager coefficient…
The content of this contribution is based on the course on numerical analysis techniques for non-linear dynamics. After introducing basic concepts as the visual analysis of trajectories in phase space and the importance of the nature of…
In this paper we consider a boundary value problem for fully fourth order nonlinear functional differential equation which contains all lower derivatives of proportional delay arguments. By the reduction of the problem to operator equation…
Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends…
The invariant manifold approach is used to explore the dynamics of a nonlinear rotor, by determining the nonlinear normal modes, constructing a reduced order model and evaluating its performance in the case of response to an initial…
In this work we study integral equations defined on the whole real line. Using a suitable Banach space, we look for solutions which satisfy some certain kind of asymptotic behavior. We will consider spectral theory in order to find fixed…