Hirota method for oblique solitons in two-dimensional supersonic nonlinear Schroedinger flow

Interaction of oblique dark solitons in two-dimensional supersonic nonlinear Schrödinger flow

We investigate the collision of two oblique dark solitons in the two dimensional supersonic nonlinear Schrödinger flow past two impenetrable obstacles. We numerically show that this collision is very similar to the dark soliton collisions in the one dimensional case. We observe that it is practically elastic and we measure the shifts of the solitons positions after their interaction.

Oblique dark solitons in supersonic flow of a Bose-Einstein condensate

In the framework of the Gross-Pitaevskii mean field approach it is shown that the supersonic flow of a Bose-Einstein condensate can support a new type of pattern--an oblique dark soliton. The corresponding exact solution of the Gross-Pitaevskii equation is obtained. It is demonstrated by numerical simulations that oblique solitons can be generated by an obstacle inserted into the flow.

二维近似量子流体中障碍物后激波流的超音速流动

Supersonic Flow Past an Obstacle in a Quasi-Two-Dimensional Lee-Huang-Yang Quantum Fluid

本文研究了量子流体在障碍物后产生的超音速流激波，通过理论分析和数值模拟验证了线性辐射波和斜暗孤子的形成机制。

Oblique spatial dispersive shock waves in nonlinear Schrödinger flows

In dispersive media, hydrodynamic singularities are resolved by coherent wavetrains known as dispersive shock waves (DSWs). Only dynamically expanding, temporal DSWs are possible in one-dimensional media. The additional degree of freedom inherent in two-dimensional media allows for the generation of time-independent DSWs that exhibit spatial expansion. Spatial oblique DSWs, dispersive analogs of oblique shocks in classical media, are constructed utilizing Whitham modulation theory for a class of nonlinear Schrödinger boundary value problems. Self-similar, simple wave solutions of the modulatio…

Two-dimensional supersonic nonlinear Schrödinger flow past an extended obstacle

Supersonic flow of a superfluid past a slender impenetrable macroscopic obstacle is studied in the framework of the two-dimensional defocusing nonlinear Schrödinger (NLS) equation. This problem is of fundamental importance as a dispersive analogue of the corresponding classical gas-dynamics problem. Assuming the oncoming flow speed sufficiently high, we asymptotically reduce the original boundary-value problem for a steady flow past a slender body to the one-dimensional dispersive piston problem described by the nonstationary NLS equation, in which the role of time is played by the stretched $…

Bright-dark vector soliton solutions for the coupled complex short pulse equations in nonlinear optics

Under investigation in this paper are the coupled complex short pulse equations, which describe the propagation of ultra-short optical pulses in cubic nonlinear media.Through the Hirota method, bright-dark one- and two-soliton solutions are obtained. Interactions between two bright or two dark solitons are verified to be elastic through the asymptotic analysis. With different parameter conditions of the vector bright-dark two solitons, the oblique interactions, bound states of solitons and parallel solitons are analyzed.