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We demonstrate the controllable generation of distinct types of dispersive shock-waves emerging in a quantum droplet bearing environment with the aid of step-like initial conditions. Dispersive regularization of the ensuing hydrodynamic…

Pattern Formation and Solitons · Physics 2024-08-20 Sathyanarayanan Chandramouli , Simeon I. Mistakidis , Garyfallia C. Katsimiga , Panayotis G. Kevrekidis

We study the propagation of narrow solitons through various profiles of dispersive shock waves (DSW) for the generalized Korteweg-de Vries equation. We consider situations in which the soliton passes through the DSW region quickly enough…

Pattern Formation and Solitons · Physics 2025-04-14 Shaykin Dmitriy

We report on the formation of a dispersive shock wave in a nonlinear optical medium. We monitor the evolution of the shock by tuning the incoming beam power. The experimental observations for the position and intensity of the solitonic edge…

Quantum Gases · Physics 2021-05-20 T. Bienaimé , M. Isoard , Q. Fontaine , A. Bramati , A. M. Kamchatnov , Q. Glorieux , N. Pavloff

The one-dimensional piston shock problem is a classical result of shock wave theory. In this work, the analogous dispersive shock wave (DSW) problem for a dispersive fluid described by the nonlinear Schr\"odinger equation is analyzed.…

Pattern Formation and Solitons · Physics 2010-08-12 M. A. Hoefer , M. J. Ablowitz , P. Engels

We present the full classification of wave patterns evolving from an initial step-like discontinuity for arbitrary choice of boundary conditions at the discontinuity location in the DNLS equation theory. In this non-convex dispersive…

Pattern Formation and Solitons · Physics 2018-01-22 A. M. Kamchatnov

It is a matter of experience that nonlinear waves in dispersive media, propagating primarily in one direction, may appear periodic in small space and time scales, but their characteristics --- amplitude, phase, wave number, etc. --- slowly…

Analysis of PDEs · Mathematics 2015-12-09 Jared C. Bronski , Vera Mikyoung Hur , Mathew A. Johnson

The Whitham modulation equations for the defocusing nonlinear Schrodinger (NLS) equation in two, three and higher spatial dimensions are derived using a two-phase ansatz for the periodic traveling wave solutions and by period-averaging the…

Pattern Formation and Solitons · Physics 2024-11-12 Asela Abeya , Gino Biondini , Mark A. Hoefer

In this Letter we present discrete wave turbulence (DWT) as a counterpart of classical statistical wave turbulence (SWT). DWT is characterized by resonance clustering, not by the size of clusters, i.e. it includes, but is not reduced to,…

Fluid Dynamics · Physics 2009-09-07 Elena Kartashova

We use the Gurevich-Pitaevskii approach based on the Whitham averaging method for studying the formation of dispersive shock waves in an intense light pulse propagating through a saturable nonlinear medium. Although the Whitham modulation…

Pattern Formation and Solitons · Physics 2020-09-23 Sergey K. Ivanov , Jules-Elemir Suchorski , Anatoly M. Kamchatnov , Mathieu Isoard , Nicolas Pavloff

We consider the step Riemann problem for the system of equations describing the propagation of a coherent light beam in nematic liquid crystals, which is a general system describing nonlinear wave propagation in a number of different…

Pattern Formation and Solitons · Physics 2016-04-27 Gennady A. El , Noel F. Smyth

The Whitham equation is a nonlocal, nonlinear partial differential equation that models the temporal evolution of spatial profiles of surface displacement of water waves. However, many laboratory and field measurements record time series at…

Fluid Dynamics · Physics 2024-11-20 John D. Carter , Diane Henderson , Panayotis Panayotaros

In this work, modulation of periodic interfacial waves on a conduit of viscous liquid is explored utilizing Whitham theory and Nonlinear Schr\"odinger (NLS) theory. Large amplitude periodic wave modulation theory does not require…

Pattern Formation and Solitons · Physics 2017-03-14 Michelle D. Maiden , Mark. A. Hoefer

Whitham theory of modulations is developed for periodic waves described by nonlinear wave equations integrable by the inverse scattering transform method associated with $2\times2$ matrix or second order scalar spectral problems. The theory…

Exactly Solvable and Integrable Systems · Physics 2007-05-23 A. M. Kamchatnov

The formation of dispersive shock waves in the one-dimensional Bose gas represents a limitation of Generalized Hydrodynamics (GHD) due to the coarse-grained nature of the theory. Nevertheless, GHD accurately captures the long wavelength…

Statistical Mechanics · Physics 2025-02-11 Frederik Møller , Philipp Schüttelkopf , Jörg Schmiedmayer , Sebastian Erne

Diffusing-Wave Spectroscopy (DWS) treats the transport of photons through turbid samples as a diffusion process, thereby making it possible to extract the dynamics of scatterers from measured correlation functions. The analysis of DWS data…

Soft Condensed Matter · Physics 2017-12-27 Zahra Fahimi , Frank Aangenendt , Panayiotis Voudouris , Johan Mattson , Hans M. Wyss

The Riemann problem for the discrete conservation law $2 \dot{u}_n + u^2_{n+1} - u^2_{n-1} = 0$ is classified using Whitham modulation theory, a quasi-continuum approximation, and numerical simulations. A surprisingly elaborate set of…

Pattern Formation and Solitons · Physics 2025-05-21 Patrick Sprenger , Christopher Chong , Emmanuel Okyere , Michael Herrmann , P. G. Kevrekidis , Mark A. Hoefer

The dependent scattering effect (DSE), which arises from the wave nature of electromagnetic radiation, is a critical mechanism affecting the radiative properties of micro/nanoscale discrete disordered media (DDM). In the last a few decades,…

Mesoscale and Nanoscale Physics · Physics 2020-09-01 B. X. Wang , C. Y. Zhao

We consider the nonlinear wave modulation of arbitrary amplitude periodic traveling wave solutions of the Ostrovsky equation, which arises as a model for the unidirectional propagation of small-amplitude, weakly nonlinear surface and…

Analysis of PDEs · Mathematics 2025-05-28 Mathew A. Johnson , Jeffrey Oregero , Wesley R. Perkins

We consider two physically and mathematically distinct regularization mechanisms of scalar hyperbolic conservation laws. When the flux is convex, the combination of diffusion and dispersion are known to give rise to monotonic and…

Pattern Formation and Solitons · Physics 2017-03-14 G. A. El , M. A. Hoefer , M. Shearer

The structure of optical dispersive shock waves in nematic liquid crystals is investigated as the power of the optical beam is varied, with six regimes identified, which complements previous work pertinent to low power beams only. It is…

Pattern Formation and Solitons · Physics 2021-12-28 Saleh Baqer , Dimitrios J. Frantzeskakis , Theodoros Horikis , Côme Houdeville , Timothy R. Marchant , Noel F. Smyth