In this article, we put a direct method to construct the rational solitary wave solutions for some nonlinear differential difference equations in mathematical physics which may be called the rational solitary wave difference method. We use the proposed method to construct the rational solitary exact solutions for some nonlinear differential difference equations via the lattice equation, the dis...

From the outset, mathematicians and physicists have been concerned with the ways in which solutions to this equation can be associated to classical particle motion, and the ways in which they cannot: the classical dynamical behavior of particles is intermixed with dispersive spreading and interference phenomena in quantum theory. More recently, nonlinear Schrödinger equations have come to play ...

A numerical investigation of nonlinear interaction mechanisms producing large wave energy concentrations, which lead to episodic transient waves, is performed using both a Higher Order Spectral (HOS) model and a three-dimensional (3D) fully nonlinear Numerical Wave Tank (NWT). Self-focusing of wave energy is achieved through modulating a periodic wave train along two orthogonal directions. Nonl...

The coexistence of two different types of fundamental rogue waves is unveiled, based on the coupled equations describing the (2+1)-component long-wave-short-wave resonance. For a wide range of asymptotic background fields, each family of three rogue wave components can be triggered by using a slight deterministic alteration to the otherwise identical background field. The ability to trigger mar...

We apply the Pancharatnam-Berry phase approach to plasmonic metasurfaces loaded by highly nonlinear multiquantum-well substrates, establishing a platform to control the nonlinear wave front at will based on giant localized nonlinear effects. We apply this approach to design flat nonlinear metasurfaces for efficient second-harmonic radiation, including beam steering, focusing, and polarization m...

A model of kinetic effects in Langmuir wave dynamics is presented using a nonlinear distribution function that includes particle separatrix crossing and self-consistent electrostatic evolution. This model is based on the adiabatic motion of electrons in the wave to describe Bernstein–Greene– Kruskal-like Langmuir waves over a wide range of temperatures 0.1 k D 0.4 . The asymptotic distribution ...

A linear theory of whistler wave is developed wihtin the paradigm of a two dimensional incompressible electron magnetohydrodynamics model. Exact analytic wave solutions are obtained for a small amplitude whistler wave that exhibit magnetic field topological structures consistent with the observations and our simulations in linear regime. In agreement with experiment, we find that the parallel g...