Related papers: Nonlinear responses from the interaction of two pr…
The analysis of nonlinear wave equations has experienced a dramatic growth in the last ten years or so. The key factor in this has been the transition from linear analysis, first to the study of bilinear and multilinear wave interactions,…
We derive the nonlinear fractional surface wave equation that governs compression waves at an interface that is coupled to a viscous bulk medium. The fractional character of the differential equation comes from the fact that the effective…
The boundary conditions at the deformable interface between two contacting fluids are derived for the general case of the large-amplitude perturbations. The interface is modeled as perturbed free boundary that evolves in time, and the…
Three dimensional nonlinear wave interactions have been analytically described. The procedure under interest can be applied to three dimensional quasilinear systems of first order, whose hydrodynamic reductions are homogeneous…
We consider nonlinear elastic wave equations generalizing Gol'dberg's five constants model. We analyze the nonlinear interaction of two distorted plane waves and characterize the possible nonlinear responses. Using the boundary measurements…
Ocean waves are complex and often turbulent. While most ocean wave interactions are essentially linear, sometimes two or more waves interact in a nonlinear way. For example, two or more waves can interact and yield waves that are much…
The topic of interface effects in wave propagation has attracted great attention due to their theoretical significance and practical importance. In this paper we study nonlinear oscillatory systems consisting of two media separated by an…
We address the properties of surface-wave solitons on the interface between a semi-infinite homogeneous linear medium and a semi-infinite homogeneous nonlinear nonlocal medium. The stability, energy flow and FWHM of the surface wave…
We study the interaction of highly nonlinear solitary waves in granular crystals, with an adjacent linear elastic medium. We investigate the effects of interface dynamics on the reflection of incident waves and on the formation of primary…
Nonlinear effects in emission and absorption spectra of gaseous systems are considered. It is shown that level splitting can be detected spectroscopically even if it is below the Doppler width. Conditions for distinguishing interference…
We predict that the interface of materials with defocusing thermal nonlinearities support stable fundamental and higher-order surface waves when the opposite edges of the medium are maintained at different temperatures. Such surface waves…
We review the scattering from non-linear interfaces containing buckling elastic beams. An illustrative example is discussed here of scattering of linear elastic pressure waves from a two-mass system connected by a non-linear structured…
We study the properties of mode-mode interactions for waves propagating in nonlinear disordered one-dimensional systems. We focus on i) the localization volume of a mode which defines the number of interacting partner modes, ii) the overlap…
We study both linear and nonlinear surface waves localized at the interface separating a left-handed medium (i.e. the medium with both negative dielectric permittivity and negative magnetic permeability) and a conventional (or right-handed)…
Using simple kinematics, we propose a general theory of linear wave interactions between the interfacial waves of a two dimensional (2D), inviscid, multi-layered fluid system. The strength of our formalism is that one does not have to…
Nonlinear waves are studied in a mixture of liquid and gas bubbles. Influence of viscosity and heat transfer is taken into consideration on propagation of the pressure waves. Nonlinear evolution equations of the second and the third order…
We demonstrate that in three space dimensions, the scattering behaviour of semilinear wave equations with quintic-type nonlinearities uniquely determines the nonlinearity. The nonlinearity is permitted to depend on both space and time.
The dynamics of phase-separated interfaces shape the behavior of both passive and active condensates. While surface tension in equilibrium systems minimizes interface length, non-equilibrium fluxes can destabilize flat or constantly curved…
We consider longwave mode of the interface instability in the system comprising of two immiscible fluid layers. The fluids fill out plane horizontal cavity which is subjected to horizontal harmonic vibration. The analysis is performed…
We consider the Hartree equation with a smooth kernel and an external potential, in the semiclassical regime. We analyze the propagation of two initial wave packets, and show different possible effects of the interaction, according to the…