Sliding-frequency filter systems are known to admit two families of accelerating solitons: high-amplitude and low-amplitude families. Such equilibrium solutions are computed here, for a wide range of filter strengths, as self-similar solutions having Airy function asymptotics. In a limited parameter region, the profile possesses a secondary small hump. The high-amplitude solitons are found to b...

In this study, based on the optimal free derivative without memory methods proposed by Cordero et al. [A. Cordero, J.L. Hueso, E. Martinez, J.R. Torregrosa, Generating optimal derivative free iterative methods for nonlinear equations by using polynomial interpolation, Mathematical and Computer Modeling. 57 (2013) 1950-1956], we develop two new iterative with memory methods for solving a nonline...

YAAKOV LUMER, YI LIANG, RAN SCHLEY, IDO KAMINER, ELAD GREENFIELD, DAOHONG SONG, XINZHENG ZHANG, JINGJUN XU, ZHIGANG CHEN, AND MORDECHAI SEGEV* Physics Department, Technion–Israel Institute of Technology, Haifa 32000, Israel MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute & School of Physics, Nankai University, Tianjin 300457, China College of Physics Science...

Braneworld models with induced gravity have the potential to replace dark energy as the explanation for the current accelerating expansion of the Universe. The original model of Dvali, Gabadadze and Porrati (DGP) demonstrated the existence of a “self–accelerating” branch of background solutions, but suffered from the presence of ghosts. We present a new large class of braneworld models which ge...

The methods that use memory using accelerating parameters for computing multiple roots are almost non-existent in the literature. Furthermore, only paper available this direction showed an increase order of convergence 0.5 from without to with extension. In paper, we introduce a new fifth-order method, which subsequently extend two higher-order self-accelerating parameter. proposed extension de...

We present the experimental observation of 1D and 2D self-accelerating nonlinear beams in quadratic media, which are also the first nonlinear self-accelerating beams in any symmetric nonlinearity. Notably, we show that the intensity peaks of the first and second harmonics are asynchronous with respect to one another, but the coupled harmonics exhibit joint acceleration within the nonlinear medi...

We present self-accelerating self-trapped beams in nonlinear optical media, exhibiting self-focusing and self-defocusing Kerr and saturable nonlinearities, as well as a quadratic response. In Kerr and saturable media such beams are stable under self-defocusing and weak self-focusing, whereas for strong self-focusing the beams off-shoot solitons while their main lobe continues to accelerate. Sel...