# Snake instability and vortex pair

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1. Dec 9, 2014

### Pring

Dark soliton is a general phynomenon in broad physics subjects. In higher dimensions, dark soliton exhibits instable except one special kind as vortex. The fundamental instability of a single dark soliton in two dimensions is to eventually decay into a number of quantized vortics through what is called the snake instability. The problem is that: what the snake instability exactly means? Someone say when the soliton in one dimension going to second dimension, due to the phase change, the dark soliton will be bend, if the curvature is large enough, the dark soliton will be split into vortex-antivortex pair. I don't know how phase change plays a role?

2. Dec 9, 2014

### soarce

From the abstract of Svortices and the fundamental modes of the “snake instability”: Possibility of observation in the gaseous Bose–Einstein Condensate, article of J. Brand: ... where soliton stripes are subject to a transverse modulational instability known as the "snake instability".

3. Dec 9, 2014

### Pring

Thank your, I am reading the paper which you have mentioned, but I think the transverse modulational instability is not clear enough in physic.

4. Dec 9, 2014

### soarce

We are talking about solitons. Before anything else maybe you should reffer to Kivshar's book Optical Solitons: From fibers to photonic crystalls section 9.7 Transverse modulation instability.

LE: The section 9.7 addresses the vector solitons, maybe is not what your were looking for.

LE2: I think that you should try to read some standard book/material on solitons which deals with the instabilities. When you have any doubt you can bring into discussion the referrence which you study.

Last edited: Dec 9, 2014
5. Dec 9, 2014

### soarce

I found this paper http://arxiv.org/pdf/1004.3060.pdf where they study how to suppress the instability of dark soliton stripes, one can see some snakes in their pictures :)
I hope it helps.

6. Dec 9, 2014

### Pring

Thank you for your detailed suggestion. The paper confused me is added underlying. Instability part is read past, maybe I should read it again.:D

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7. Dec 9, 2014

### soarce

I had a quick look at the paper you posted. Indeed, it can be misleading when they speak of snake instability. I think that, generally, snake instability is releated mainly with long wavelength perturbation modes which they suppress in they set-up by adjusting the scattering length g. Probably, the "snake perturbation" of more complex soliton structures doesn't have an intuitive behaviour or visual interpretation, e.g. curves the soliton stripe and turns it into a "snake".

The structures they study in this article seems to me to be more like quadrupole or multipole solitons, in figure 1 the dark blue background stands for zero or for non-zero value? If it is zero then it is improper to speak of dark solitons, they would have bright solitons. Then they perform standard linear stability analysis and found that beside the snake instability there exists other one(s). This result is of no surprize, the multipole soliton structures are highly unstable.

8. Apr 1, 2015

### Pring

Thank you. In this paper, why the eigenvalue of L should be positive in the formula (A10)?

9. Apr 8, 2015

### soarce

In this case the operator $L$ is hermitian (diagonal form with real numbers) and its eigenvalues are real, where did they say that the eigenvalues are positive? It may have all eigenvalues positive and this implies that all perturbation modes are either growing or suppressed (depending on the sign convention in the paper), or oscillatory (depending on the real and imaginary part convention of the eigenvalue of the linear perturbation mode), I need to check the derivation of their equations.