Resonant generation and refraction of dispersive shock waves in one-dimensional nonlinear Schrödinger flows
In the Thesis, two important theoretical problems arising in the theory of one-dimensional defocusing nonlinear Schrodinger (NLS) flows are investigated analytically and numerically: (i) the resonant…
Soliton-mean field interaction in Korteweg-de Vries dispersive hydrodynamics
- Physics, Mathematics
The propagation of localized solitons in the presence of large-scale waves is a fundamental problem, both physically and mathematically, with applications in fluid dynamics, nonlinear optics and…
Propagation of solitary waves and undular bores over variable topography
Description of the interaction of a shallow-water wave with variable topography is a classical and fundamental problem of fluid mechanics. The behaviour of linear waves and isolated solitary waves…
HYDRODYNAMIC TYPE SYSTEMS AND THEIR INTEGRABILITY Introduction for Applied Mathematicians
Hydrodynamic type systems are systems of quasilinear equations of the first order. They naturally arise in continuum mechanics but also occur as a result of semi-classical approximations of nonlinear…
Transformation of a shoaling undular bore
- PhysicsJournal of Fluid Mechanics
Abstract We consider the propagation of a shallow-water undular bore over a gentle monotonic bottom slope connecting two regions of constant depth, in the framework of the variable-coefficient…
The Existence Solution to the Development Wave Equation With Arbitrary Conditions
- Mathematics, Education
We study the development wave equation with some conditions and proving theexistence and uniqueness solution by using the reflection method . Keywords: Wave equation, Mathematica, reflection method.
SHOWING 1-10 OF 76 REFERENCES
Resolution of a shock in hyperbolic systems modified by weak dispersion.
We present a way to deal with dispersion-dominated "shock-type" transition in the absence of completely integrable structure for the systems that one may characterize as strictly hyperbolic…
Dispersive and classical shock waves in Bose-Einstein condensates and gas dynamics
A Bose-Einstein condensate (BEC) is a quantum fluid that gives rise to interesting shock-wave nonlinear dynamics. Experiments depict a BEC that exhibits behavior similar to that of a shock wave in a…
Piston dispersive shock wave problem.
- PhysicsPhysical review letters
In this work, the analogous dispersive shock wave (DSW) problem for a fluid described by the nonlinear Schrödinger equation is analyzed and asymptotic solutions are calculated for a piston moving with uniform speed into a dispersive fluid at rest.
Dissipationless shock waves in media with positive dispersion
- Physics, Mathematics
We consider nonstationary one-dimensional flows in dissipationless hydrodynamics with positive dispersion which is described by the nonlinear Schrodinger equation. We determine the conditions for the…
Asymptotic soliton train solutions of the defocusing nonlinear Schrödinger equation.
- Physics, MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
Good agreement of the numerical solution of the defocusing NLS equation with predictions of the asymptotic theory is found.
Theory of optical dispersive shock waves in photorefractive media
The theory of optical dispersive shocks generated in the propagation of light beams through photorefractive media is developed. A full one-dimensional analytical theory based on the Whitham…
Two-dimensional supersonic nonlinear Schrödinger flow past an extended obstacle.
- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
An extension of the traditional modulation description of DSWs to include the linear "ship-wave" pattern forming outside the nonlinear modulation region of the front DSW, which is relevant to recent experiments on Bose-Einstein condensates freely expanding past obstacles.
Generation of undular bores in the shelves of slowly-varying solitary waves.
The nonlinear evolution of the shelves is described in terms of exact solutions to the KdV-Whitham equations with natural boundary conditions for the Riemann invariants, which describe the generation of small "secondary" solitary waves in the trailing shelves.
Flow of a Bose-Einstein condensate in a quasi-one-dimensional channel under the action of a piston
The problem of the flow of a Bose—Einstein condensate in a channel under the action of a piston is considered. Problems of this kind are topical in connection with experiments on condensate flow…