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We apply variational-wavelet approach for constructing multiscale high-localized eigenmodes expansions in different models of nonlinear waves. We demonstrate appearance of coherent localized structures and stable pattern formation in…
We develop a diagrammatic theory for transport of waves in disordered media with weak nonlinearity. We first represent the solution of the nonlinear wave equation as a nonlinear Born series. From this, we construct nonlinear ladder and…
The paper presents new results on localisation and transmission of flexural waves in a structured plate containing a semi-infinite two-dimensional array of rigid pins. In particular, surface waves are identified and studied at the interface…
Nonlinear plane acoustic waves propagating through a fluid are studied using Burgers' equation with finite viscosity. The evolution of a simple N-pulse with regular and random initial amplitude and of pulses with monochromatic and noise…
The propagation of waves in the nonlinear acoustic metamaterials (NAMs) is fundamentally different from that in the conventional linear ones. In this article we consider two one-dimensional NAM systems featuring respectively a diatomic and…
A theory of electromagnetic wave propagation in a weakly anisotropic smoothly inhomogeneous medium is developed, based on the quantum-mechanical diagonalization procedure applied to Maxwell equations. The equations of motion for the…
Wave dynamics in topological materials has been widely studied recently. A striking feature is the existence of robust and chiral wave propagations that have potential applications in many fields. A common way to realize such wave patterns…
A general localization mechanism for waves in dissipative systems is identified that does not require the bistability of the basic state and the nonlinear plane-wave state. The mechanism explains the two-dimensional localized wave…
We analyze mechanisms and regimes of wave packet spreading in nonlinear disordered media. We predict that wave packets can spread in two regimes of strong and weak chaos. We discuss resonance probabilities, nonlinear diffusion equations,…
Wave propagation in time-varying media has attracted significant attention for its innovative potential to control wave-matter interactions and to develop versatile active materials. While most research has focused on electromagnetic waves,…
Using the very basic physics principles, we have studied the implications of quantum corrections to classical electrodynamics and the propagation of electromagnetic waves and pulses. The initial nonlinear wave equation for the…
We study the nonlinear wave dynamics of one-dimensional chains of polycatenated rings. These interlocked structures support amplitude-dependent nonlinear wave propagation driven by tensile activation and internal structural flexibility,…
Propagation-invariant or non-diffracting optical beams have received considerable attention during the last two decades. However, the pulsed nature of light waves and the structured property of optical media like waveguides are often…
We have developed a new family of limited-diffraction electromagnetic X-shaped waves based on the scalar "X waves" discovered previously. These waves are diffraction-free in theory and particle-like (wave packets), in that they maintain…
The propagation of waves through microstructured media with periodically arranged inclusions has applications in many areas of physics and engineering, stretching from photonic crystals through to seismic metamaterials. In the…
Nonlinear optical media that are normally dispersive, support a new type of localized (nondiffractive and nondispersive) wavepackets that are X-shaped in space and time and have slower than exponential decay. High-intensity X-waves, unlike…
The so-called Localized Waves (LW), and the "Frozen Waves" (FW), have arisen significant attention in the areas of Optics and Ultrasound, because of their surprising energy localization properties. The LWs resist the effects of diffraction…
We investigate the propagation of Rayleigh waves in a half-space coupled to a nonlinear metasurface. The metasurface consists of an array of nonlinear oscillators attached to the free surface of a homogeneous substrate. We describe,…
We generalize the invariant imbedding theory of the wave propagation and derive new invariant imbedding equations for the propagation of arbitrary number of coupled waves of any kind in arbitrarily-inhomogeneous stratified media, where the…
Steady-state and transient antiplane dynamic processes in a structured solids consisting of uniform periodic square-cell lattices connected by a lattice layer of different bond stiffnesses and point masses are analyzed. A semi-infinite…