We analyse systematically, from the viewpoint of the nonlinear physics of solitary waves, the effect of the spatial dimension (D = 1, 2, 3) on the structure and stability of the Bose-Einstein condensates (BECs) trapped in an external anisotropic parabolic potential. While for the positive scattering length the stationary ground-state solutions of the Gross-Pitaevskii equation are shown to be al...

Non-invasively focusing light into strongly scattering media, such as biological tissue, is highly desirable but challenging. Recently, ultrasonically guided wavefront shaping technologies have been developed to address this limitation. So far, the focusing resolution of most implementations has been limited by acoustic diffraction. Here, we introduce nonlinear photoacoustically guided wavefron...

In this paper, we prove the nonlinear orbital stability of the stationary traveling wave of the one-dimensional Gross-Pitaevskii equation by using Zakharov-Shabat’s inverse scattering method.

In this paper, we investigate the homogenization of a nonlinear kinetic equation modeling electron transport in semiconductors. We compute effective scattering coefficients for medium with periodic inhomogeneities.

In this paper, we investigate the homogenization of a nonlinear kinetic equation modeling electron transport in semiconductors. We compute effective scattering coefficients for medium with periodic inhomogeneities.

Fluorescence-free microscopy: A new nonlinear optical microspectroscopy technique, femtosecond (fs) triple-resonance coherent anti-Stokes Raman scattering, in which the amplitude and phase of input fs laser pulses are optimally shaped to be in triple resonance with the molecular electronic and vibrational transitions, generates a coherent nonlinear signal beam at a new color with a highest poss...

Whitham theory of modulations is developed for periodic waves described by nonlinear wave equations integrable by the inverse scattering transform method associated with 2 × 2 matrix or second order scalar spectral problems. The theory is illustrated by derivation of the Whitham equations for perturbed Korteweg-de Vries equation and nonlinear Schrödinger equation with linear damping.

This paper constructs translation-invariant operators on L2.Rd /, which are Lipschitz-continuous to the action of diffeomorphisms. A scattering propagator is a path-ordered product of nonlinear and noncommuting operators, each of which computes the modulus of a wavelet transform. A local integration defines a windowed scattering transform, which is proved to be Lipschitz-continuous to the actio...

High quality (Q) factor whispering gallery modes (WGMs) can induce nonlinear effects in liquid droplets through mechanisms such as radiation pressure, light scattering, thermocapillarity, Kerr nonlinearity, and thermal effect. However, such nonlinear effects have yet to be thoroughly investigated and compared in the literature. In this study, we first investigate a micron-sized liquid spherical...

Migration is a seismic imaging method that consists of creating a representation of the Earth’s subsurface structure from the recording of seismic waves. Migration is essentially equivalent to solving an inverse scattering problem in structurally complex media. Conventional migration algorithms rely on linearized inversion schemes and assume single-scattering dominance. The primary focus of thi...