We consider an equation with exponential nonlinearity under the Dirichlet boundary condition. For a one- or two-dimensional domain, global solution has been obtained. In this paper, to extend result higher dimensional case, we concentrate on radial solutions in annulus. First, construct time-local abstract theory of differential equations. Next, show that decreasing energy exists problem. Final...

A novel design of Dual-Core Photonic Crystal Fiber (DC-PCF) with silica-air microstructures is proposed in this paper. Nonlinearity and confinement loss of DC-PCF are evaluated by using a Full-Vectorial Finite Element Method (FV-FEM) successfully. By optimizing the geometry of three ring DC-PCFs, a high nonlinearity (52w-1km-1) and low confinement loss (0.001dB/km) can be achieved at 1.55μm wav...

bifurcations leading to chaos have been investigated in a number of one dimensional dynamical systems by varying the parameters incorporated within the systems. the property hyperbolicity has been studied in detail in each case which has significant characteristic behaviours for regular and chaotic evolutions. in the process, the calculations for invariant set have also been carried out. a bro...

Abstract: In this paper, a method for determination of refractive index in membrane of fuel cell on basis of three-longitudinal-mode laser heterodyne interferometer is presented. The optical path difference between the target and reference paths is fixed and phase shift is then calculated in terms of refractive index shift. The measurement accuracy of this system is limited by nonlinearity erro...

We propose a new approach that allows one to reduce nonlinear equations on Lie groups with fewer number of independent variables for finding particular solutions the equations. The main idea is apply method noncommutative integration linear part equation, which find bases in space partial differential set noncommuting symmetry operators. implemented generalized Schrödinger equation group curved...

In the present work we obtain existence and multiplicity of nontrivial solutions for Choquard logarithmic equation $(-\Delta)_{p}^{s}u + |u|^{p-2}u (\ln|\cdot|\ast |u|^{p})|u|^{p-2}u = f(u) \textrm{ \ in } \mathbb{R}^N $ , where N=sp $, s\in (0, 1) p>2 a>0 \lambda >0 $f: \mathbb{R}\rightarrow \mathbb{R} a continuous nonlinearity with exponential critical subcritical growth. We guarantee solutio...