In this paper, Heir-equations method is applied to investigate nonclassical symmetries and new solutions of the Black-Scholes equation. Nonlinear self-adjointness is proved and infinite number of conservation laws are computed by a new conservation laws theorem.

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...

Nowadays, atomic force microscope is considered as a useful tool in the determination of intermolecular forces and surface topography with the resolution of nanometers. In this kind of microscope, micro cantilever is considered as the heart of the microscope and is used as a measuring tool.  This paper is aimed towards investigating the behavior of a piezoelectric micro cantilever with a triang...

An important group of nonlinear processes in optical fibre involves the mixing of four waves due to the intensity dependence of the refractive index. It is customary to distinguish between nonlinear effects that require external/pumping waves (cross-phase modulation and parametric processes such as four-wave mixing) and self-action of the propagating optical field (self-phase modulation and mod...