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A periodic two-phase algebro-geometric solution of the focusing nonlinear Schr\"odinger equation is constructed in terms of elliptic Jacobi theta-functions. A dependence of this solution on the parameters of a spectral curve is…
The averaging method combined with the Lyapunov-Schmidt reduction provides sufficient conditions for the existence of periodic solutions of the following class of perturbative $T$-periodic nonautonomous differential equations…
We contribute to the method of trigonometric series for solving differential equations of certain non linear oscillators. Key Words: series power solution, trigonometric series.
The existence of periodic solutions is proven for some neuroscience models with a small parameter. Moreover, the stability of such solutions is investigated, as well. The results are based on a theoretical research dealing with the…
We shall deal with the periodic problem for nonlinear perturbations of abstract hyperbolic evolution equations generating an evolution system of contractions. We prove an averaging principle for the translation along trajectories operator…
We consider existence and stability of an almost periodic solution of the quasilinear system of differential equations with piecewise constant argument of generalized type. The associated linear homogeneous system satisfies exponential…
In this study, we focus on the existence of a periodic solution for the neutral nonlinear dynamic systems with delay% \[ x^{\Delta}(t)=A(t)x(t)+Q^{\Delta}\left(t,x\left(\delta_{-}(s,t)\right) \right)…
For a number of nonlocal nonlinear equations such as nonlocal, nonlinear Schr\"odinger equation (NLSE), nonlocal Ablowitz-Ladik (AL), nonlocal, saturable discrete NLSE (DNLSE), coupled nonlocal NLSE, coupled nonlocal AL and coupled…
We consider the nonlinear Schroedinger equation in higher dimension with Dirichlet boundary conditions and with a non-local smoothing nonlinearity. We prove the existence of small amplitude periodic solutions. In the fully resonant case we…
In this work we study the existence of periodic and asymptotically periodic solutions of a system of nonlinear Volterra difference equations with infinite delay. By means of fixed point theory, we furnish conditions that guarantee the…
Meromorphic solutions of autonomous nonlinear ordinary differential equations are studied. An algorithm for constructing meromorphic solutions in explicit form is presented. General expressions for meromorphic solutions (including rational,…
Stochastic-periodic homogenization is studied for the Maxwell equations with nonlinear and periodic electric conductivity. It is shown by the stochastic-two-scale convergence method that the sequence of solutions of a class of highly…
We prove the existence of exponentially localised and time-periodic solutions in general nonlinear Hamiltonian lattice systems. Like normal modes, these localised solutions are characterised by collective oscillations at the lattice sites…
We prove the well-posedness results, i.e. existence, uniqueness, and stability, of the solutions to a class of nonlocal fully nonlinear parabolic partial differential equations (PDEs), where there is an external time parameter $t$ on top of…
In this paper, we investigate the asymptotic dynamics of Fisher-KPP equations with nonlocal dispersal operator and nonlocal reaction term in time periodic and space heterogeneous media. We first show the global existence and boundedness of…
Many biological and engineering materials have nonperiodic microstructures for which classical periodic homogenization results do not apply. Certain nonperiodic microstructures may be approximated by locally periodic microstructures for…
In this paper, we establish some sufficient conditions for the existence of stable random periodic solutions of stochastic differential equations and ergodicity in the random periodic regime. The techniques involve the existence of Lyapunov…
In this article we discuss the long-time dynamics of the radial solutions to the focusing energy-critical wave equation in 5-dimensional space. We give some details about the asymptotic behaviour, topological structure and time evolution of…
The following document presents a possible solution and a brief stability analysis for a nonlinear system, which is obtained by studying the possibility of building a hybrid solar receiver; It is necessary to mention that the solution of…
By a refinement of the technique used by Johnson and Zumbrun to show stability under localized perturbations, we show that spectral stability implies nonlinear modulational stability of periodic traveling-wave solutions of reaction…