arXiv subjects

Ysla F. Adans

Publications and source records attributed to Ysla F. Adans.

3 recordsLinked to original sources

arXiv2026

On deforming and breaking integrability

In this paper we study nearest-neighbour deformations of integrable models. After expanding in the deformation parameter, we identify four possible types of deformations. First there are deformations that simply break or preserve integrability. Then we find two different subtle cases. The first case is where the deformation is only integrable if all orders of the deformation parameter are taken into account. An example of these are the long-range deformations that appear in holographic models. The second case is when the deformation is perturbatively integrable to some order in the deformation parameter but can not be extended to an integrable model. In this paper we work this out for the XXZ spin chain and discuss the level statistics of each of these cases. We find numerical evidence that the onset of chaos occurs differently in each of these models. For the perturbatively integrable models, we find that the deformation strength at which chaos appears demonstrates a volume-scaling intermediate between strong and weak integrability breaking models.

cond-mat.stat-mech↗

arXiv2023

Complex KdV rogue waves from gauge-Miura transformation

The gauge-Miura correspondence establishes a map between the entire KdV and mKdV hierarchies, including positive and also negative flows, from which new relations besides the standard Miura transformation arise. We use this correspondence to classify solutions of the KdV hierarchy in terms of elementary tau functions of the mKdV hierarchy under both zero and nonzero vacua. We illustrate how interesting nonlinear phenomena can be described analytically from this construction, such as ``rogue waves'' of a complex KdV system that corresponds to a limit of a vector nonlinear Schrödinger equation.

nlin.SI↗

arXiv2023

Negative flows of generalized KdV and mKdV hierarchies and their gauge-Miura transformations

The KdV hierarchy is a paradigmatic example of the rich mathematical structure underlying integrable systems and has far-reaching connections in several areas of theoretical physics. While the positive part of the KdV hierarchy is well known, in this paper we consider an affine Lie algebraic construction for its negative part. We show that the original Miura transformation can be extended to a gauge transformation that implies several new types of relations among the negative flows of the KdV and mKdV hierarchies. Contrary to the positive flows, such a ``gauge-Miura'' correspondence becomes degenerate whereby more than one negative mKdV model is mapped into a single negative KdV model. For instance, the sine-Gordon and another negative mKdV flow are mapped into a single negative KdV flow which inherits solutions of both former models. The gauge-Miura correspondence implies a rich degeneracy regarding solutions of these hierarchies. We obtain similar results for the generalized KdV and mKdV hierachies constructed with the affine Lie algebra $\widehat{s\ell}(r+1)$. In this case the first negative mKdV flow corresponds to an affine Toda field theory and the gauge-Miura correspondence yields its KdV counterpart. In particular, we show explicitly a KdV analog of the Tzitzéica-Bullough-Dodd model. In short, we uncover a rich mathematical structure for the negative flows of integrable hierarchies obtaining novel relations and integrable systems.

nlin.SI↗