## 7 Citations

### Resonant generation and refraction of dispersive shock waves in one-dimensional nonlinear Schrödinger flows

- Physics
- 2011

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
- 2022

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

- Physics
- 2012

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

- Mathematics
- 2014

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
- 2012

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
- 2013

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.

## References

SHOWING 1-10 OF 76 REFERENCES

### Resolution of a shock in hyperbolic systems modified by weak dispersion.

- MathematicsChaos
- 2005

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

- Physics
- 2006

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
- 2008

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
- 2009

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
- 2002

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

- Physics
- 2007

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
- 2009

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.

- PhysicsChaos
- 2002

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

- Physics
- 2010

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…