Stability of nonlinear multiresolution analysis

Solution and stability analysis of coupled nonlinear Schrodinger equations

We consider a new type of integrable coupled nonlinear Schrodinger (CNLS)equations proposed by our self [submitted to Phys. Plasmas (2011)]. The explicitform of soliton solutions are derived using the Hirota's bilinear method.We show that the parameters in the CNLS equations only determine the regionsfor the existence of bright and dark soliton solutions. Finally, throughthe linear stability an...

Stability analysis of fractional-order nonlinear Systems via Lyapunov method

‎In this paper‎, ‎we study stability of fractional-order nonlinear dynamic systems by means of Lyapunov‎ ‎method‎. ‎To examine the obtained results‎, ‎we employe the developed techniques on test examples‎.

Nonlinear Multiresolution Image Blending

We study contrast enhancement for multiresolution image blending. In image compositing, image stitching, and image fusion, a blending operator combines coefficients of a pixel array, an image pyramid, a wavelet decomposition, or a gradient domain representation. Linear interpolation reduces variation and thereby causes contrast loss, while coefficient selection increases variation and thereby c...

The theory of matrix-valued multiresolution analysis frames

Extension of Higher Order Derivatives of Lyapunov Functions in Stability Analysis of Nonlinear Systems

The Lyapunov stability method is the most popular and applicable stability analysis tool of nonlinear dynamic systems. However, there are some bottlenecks in the Lyapunov method, such as need for negative definiteness of the Lyapunov function derivative in the direction of the system’s solutions. In this paper, we develop a new theorem to dispense the need for negative definite-ness of Lyapunov...