Related papers: The piston dispersive shock wave problem
A full analysis of all regimes for optical dispersive shock wave (DSW) propagation in nematic liquid crystals is undertaken. These dispersive shock waves are generated from step initial conditions for the optical field and are resonant in…
The viscously dominated, low Reynolds' number dynamics of multi-phase, compacting media can lead to nonlinear, dissipationless/dispersive behavior when viewed appropriately. In these systems, nonlinear self-steepening competes with wave…
The problem of wave breaking during its propagation in the Bose-Einstein condensate to a stationary medium is considered for the case when the initial profile at the breaking instant can be approximated by a power function of the form…
The propagation of the dispersive shock waves (DSWs) is investigated in the cylindrical Gardner (cG) equation, which is obtained by employing a similarity reduction to the two space one time (2+1) dimensional Gardner-Kadomtsev-Petviashvili…
We propose the suppression of dispersive spreading of wave packets governed by the free-space Schr\"odinger equation with a periodically pulsed nonlinear term. Using asymptotic analysis, we construct stroboscopically-dispersionless quantum…
Dispersive shock waves (DSWs) in the Kadomtsev-Petviashvili (KP) equation and two dimensional Benjamin-Ono (2DBO) equation are considered using parabolic front initial data. Employing a front tracking type ansatz exactly reduces the study…
We theoretically describe the quasi one-dimensional transverse spreading of a light pulse propagating in a nonlinear optical material in the presence of a uniform background light intensity. For short propagation distances the pulse can be…
We introduce and systematically investigate the generation of dispersive shock waves, which arise naturally in physical settings such as optical waveguide arrays and superfluids confined within optical lattices. The underlying physically…
We suggest a method for calculation of parameters of dispersive shock waves in framework of Whitham modulation theory applied to non-integrable wave equations with a wide class of initial conditions corresponding to propagation of a pulse…
The formation and properties of envelope dispersive shock wave (DSW) excitations from repulsive nonlinear waves in a magnetic film are studied. Experiments involve the excitation of a spin-wave step pulse in a low-loss magnetic…
This paper probes the dispersive shock waves (DSWs) theory in nonlinear optical systems through Whitham modulation theory for the high-order Chen-Lee-Liu (HOCLL) equation. We systematically derived the one-phase periodic solutions and the…
In this paper, we study detonation wave solutions to one-dimensional piston problem for the Zeldovich-von Neumann-D{\"o}ring (ZND) combustion model with a one-step exothermic chemical reaction. As a special type of shock wave, the position…
We discuss the problem of breaking of a nonlinear wave in the process of its propagation into a medium at rest. It is supposed that the profile of the wave is described at the breaking moment by the function $(-x)^{1/n}$ ($x<0$, positive…
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…
Dissipationless shock waves in modulational unstable one-dimensional medium are investigated on the simplest example of integrable focusing nonlinear Schr\''odinger (NS) equation. Our approach is based on the construction of special exact…
The possibility of finite-time, dispersive blow up for nonlinear equations of Schroedinger type is revisited. This mathematical phenomena is one of the possible explanations for oceanic and optical rogue waves. In dimension one, the…
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…
We present a method to compute dispersive shock wave solutions of the Korteweg-de Vries equation that emerge from initial data with step-like boundary conditions at infinity. We derive two different Riemann-Hilbert problems associated with…
In this work, we investigate non-classical wavetrain formations, and particularly dispersive shock waves (DSWs), or undular bores, in systems exhibiting non-convex dispersion. Our prototypical model, which arises in shallow water wave…
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…