Some preliminaries about the integrable families of Riccati equations and solutions structure of these equations in several cases are presented in this paper, then by using of definitions for fractional derivative we apply the new extended of tanh method to the perturbed nonlinear fractional Schrodinger equation with the kerr law nonlinearity. Finally by using of this method and solutions of Ri...

Stationary structures in two-dimensional Heisenberg ferromagnets. Abstract Stationary structures in a classical isotropic two-dimensional Heisenberg ferromagnetic are studied in the framework of the (2+1)-dimensional Landau-Lifshitz model. It is established that in the case of S(r, t) = S(r − vt) the Landau-Lifshitz equation is closely related to the Ablowitz-Ladik hierarchy. This relation is u...

A novel nonlocal nonlinear diffusion is analyzed which has proven useful as a denoising tool in image processing. The equation can be viewed as a new paradigm for the regularization of the well-known Perona-Malik equation. The regularization is implemented via nonlinearity intensity reduction through fractional derivatives. Well-posedness in the weak setting is established. Global existence and...

We investigate numerically the two dimensional travelling waves of the Nonlinear Schrödinger Equation for a general nonlinearity and with nonzero condition at infinity. In particular, we are interested in the energy-momentum diagrams. We propose a numerical strategy based on the variational structure of the equation. The key point is to characterize the saddle points of the action as minimizers...

ABSTRACT In this article, we propose the application of a modified Taylor series method (MTSM) for the approximation of nonlinear problems described on finite intervals. The issue of Taylor series method with mixed boundary conditions is circumvented using shooting constants and extra derivatives of the problem. In order to show the benefits of this proposal, three different kinds of problems a...

Using the path-integral technique we examine the mutual information for the communication channel modeled by the nonlinear Schrödinger equation with additive Gaussian noise. The nonlinear Schrödinger equation is one of the fundamental models in nonlinear physics, and it has a broad range of applications, including fiber optical communications-the backbone of the internet. At large signal-to-noi...

In this paper we give an extension of the Birkhoff–Lewis theorem to some semilinear PDEs. Accordingly we prove existence of infinitely many periodic orbits with large period accumulating at the origin. Such periodic orbits bifurcate from resonant finite dimensional invariant tori of the fourth order normal form of the system. Besides standard nonresonance and nondegeneracy assumptions, our main...

Abstract. In this paper the stability of equilibrium points of the nonlinear differential equation with fractional nonlinearity is studied. It is supposed that this system is exposed to additive stochastic perturbations that are of the type of white noise and are directly proportional to the deviation of the system state from the equilibrium point. Sufficient conditions for stability in probabi...

Pointing out the difference between the Discrete Nonlinear Schrödinger equation with the classical power law nonlinearity-for which solutions exist globally, independently of the sign and the degree of the nonlinearity, the size of the initial data and the dimension of the lattice-we prove either global existence or nonexistence in time, for the Discrete Klein-Gordon equation with the same type...

The uniqueness of positive solution for a class of singular fractional differential system with integral boundary conditions is considered in this paper and many types of equation system are contained in this equation system because there are many parameters which can be changeable in this equation system. The fractional orders are involved in the nonlinearity of the boundary value problem and ...