In this paper, the localized TM surface waves of a nonlinear self-focusingleft-handed slab sandwiched between a uniform medium and a one-dimensionalphotonic crystal (1D PC) is analytically investigated. Our method is based on the firstintegral of the nonlinear Maxwell's equations. For the TM surface waves, the presenceof two electric field components makes the analysis difficult. Therefore, we ...

We describe examples of hyperbolic surface waves and discuss their connection with initial boundary value and discontinuity problems for hyperbolic systems of PDEs that are weakly but not uniformly stable.

We study both linear and nonlinear surface waves localized at the interface separating a left-handed (LH) medium (i.e., a medium with both negative dielectric permittivity and negative magnetic permeability) and a conventional [or right-handed (RH)] dielectric medium. We demonstrate that the interface can support both TE- and TM-polarized surface waves-surface polaritons, and we study their pro...

We prove short-time existence of smooth solutions for a class of nonlinear, and generally spatially nonlocal, Hamiltonian evolution equations that describe the self-interaction of weakly nonlinear scale-invariant waves. These equations include ones that describe weakly nonlinear hyperbolic surface waves, such as nonlinear Rayleigh waves in elasticity.

Using the statistical characteristics is one of the methods to justify the random nature of the ocean waves. Probability function are used to facilitate the studies of the random waves parameters, such as the surface and height and period of the waves. Since, the force of the ocean waves are the prevalent principal forces on the offshore structures, the assignment of the significant structural ...