We have developed an imaging method for locating isolated nonlinear scattering source~s! in solids. It relies on extracting the nonlinear response of a solid by modulation of a high by a low-frequency wave, and employing moving-window, synchronous detection. The resulting image consists of nonlinear wave reflection profiles with remarkable sensitivity to an isolated elastic nonlinear source~s!....

Unidirectional deep-water waves are studied theoretically and experimentally. Theoretically we apply the theory of the nonlinear Schroedinger equation (NLS) using the inverse scattering transform, a kind of generalized, nonlinear Fourier analysis. We discover from the theoretical study that there are essentially four kinds of physical effects that can lead to extreme waves: (1) the superpositio...

In this present work we applied new applications of direct algebraic method to foam drainage equation and to Nonlinear Wave equation with the fifth order nonlinear term, the balance numbers of which are not positive integers. Then new types of complex solutions are obtained to the foam drainage equation and Nonlinear Wave equation with the fifth order nonlinear term.

Nonlinear dynamics of wave packets in parity-time-symmetric optical lattices near the phase-transition point is analytically studied. A nonlinear Klein-Gordon equation is derived for the envelope of these wave packets. A variety of phenomena known to exist in this envelope equation are shown to also exist in the full equation, including wave blowup, periodic bound states, and solitary wave solu...

The magnetic energy of nonlinear Alfvén waves in compressible plasmas may be ponderomotively coupled only to ion-acoustic quasi-modes which modulate the wave phase velocity and cause wave-front steepening. In the collisionless plasma with β 6= 0, the dynamics of nonlinear Alfvén wave is also affected by the resonant particle-wave interactions. Upon relatively rapid evolution (compared to the pa...

This work continues our studies of nonlinear evolution of a system of wavepackets. We study a wave propagation governed by a nonlinear system of hyperbolic PDE's with constant coefficients with the initial data being a multi-wavepacket. By definition a general wavepacket has a well defined principal wave vector, and, as we proved in previous works, the nonlinear dynamics preserves systems of wa...

This work continues our studies of nonlinear evolution of a system of wavepackets. We study a wave propagation governed by a nonlinear system of hyperbolic PDE's with constant coefficients with the initial data being a multi-wavepacket. By definition a general wavepacket has a well defined principal wave vector, and, as we proved in previous works, the nonlinear dynamics preserves systems of wa...

The 11-parameter transformation group with generators (2) and (5) is called the extended Poincaré group P̃ (1, 3). The above result admits the following group-theoretical interpretation: on the set of solutions of the nonlinear wave equation (1) two inequivalent representations of the extended Poincaré group are realized. Each representation gives rise to a P̃ (1, 3)nonlinear wave equation with a...