A nonlinear PDE-based image restoration approach is described in this article. The proposed filtering technique is based on a novel fourth-order diffusion model. Unlike many other fourth-order PDE denoising schemes, this nonlinear model provides an optimal trade-off between noise removal, image detail preservation and avoiding of undesired effects. A rigorous mathematical investigation of the w...

It is demonstrated, by means of analogue electronic simulation and theoretically, that external noise can markedly change the character of the response of a nonlinear system to a low-frequency periodic field. In general, noise of sufficient intensity linearises the response. For certain parameter ranges in particular cases, however, an increase in the noise intensity can sometime have the oppos...

It is found that the response of a nonlinear dynamical system can be linearised, and its frequency dispersion diminished, by the addition of external noise of sufficient intensity. Taking as an example an overdamped bistable system driven by a low-frequency periodic field, this noise-induced linearisation is investigated through analogue electronic experiments. The wider implications are consid...

In this paper we prove the global solvability of a class of fourth-order nonlinear boundary value problems that govern the deformation of a Hollomon’s power-law plastic beam subject to an axial compression and nonlinear lateral constrains. For certain ranges of the acting axial compression force, the solvability of the equations follows from the monotonicity of the fourth order nonlinear differ...

asymptotically exact and nonlocal fourth order nonlinear evolution equations are derived for two coupled fourth order nonlinear evolution equations have been derived in deep water for two capillary-gravity wave packets propagating in the same direction in the presence of wind flowing over water.we have used a general method, based on zakharov integral equation.on the basis of these evolution eq...

Asymptotically exact and nonlocal fourth order nonlinear evolution equations are derived for two coupled fourth order nonlinear evolution equations have been derived in deep water for two capillary-gravity wave packets propagating in the same direction in the presence of wind flowing over water.We have used a general method, based on Zakharov integral equation.On the basis of these evolution eq...

in this paper, we present two new families of third-order and fourth-order methods for finding multiple roots of nonlinear equations. each of them requires one evaluation of the function and two of its first derivative per iteration. several numerical examples are given to illustrate the performance of the presented methods.

New oscillation criteria for certain fourth order nonlinear dynamic equations with nonlinear middle term are established. Mathematics subject classification (2010): 34K11, 39A10, 39A99, 34C10, 34C15, 34N05.

We investigate efficient fourth-harmonic generation in a single two-dimensional (2D) quadratically nonlinear photonic crystal. We propose a novel parametric process that starts with phase-matched generation of a pair of symmetric second-harmonic waves, which then interact to produce a fourth-harmonic wave that is collinear to the fundamental. We show that this process is more efficient than con...