تقرير
Non-commutative NLS-type hierarchies: dressing & solutions
| العنوان: | Non-commutative NLS-type hierarchies: dressing & solutions |
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| المؤلفون: | Doikou, Anastasia, Findlay, Iain, Sklaveniti, Spyridoula |
| المصدر: | Nucl. Phys. B941 (2019) 376 |
| سنة النشر: | 2018 |
| المجموعة: | Mathematics High Energy Physics - Theory Mathematical Physics Nonlinear Sciences |
| مصطلحات موضوعية: | Mathematical Physics, High Energy Physics - Theory, Nonlinear Sciences - Exactly Solvable and Integrable Systems |
| الوصف: | We consider the generalized matrix non-linear Schrodinger (NLS) hierarchy. By employing the universal Darboux-dressing scheme we derive solutions for the hierarchy of integrable PDEs via solutions of the matrix Gelfand-Levitan-Marchenko equation, and we also identify recursion relations that yield the Lax pairs for the whole matrix NLS-type hierarchy. These results are obtained considering either matrix-integral or general $n^{th}$ order matrix-differential operators as Darboux-dressing transformations. In this framework special links with the Airy and Burgers equations are also discussed. The matrix version of the Darboux transform is also examined leading to the non-commutative version of the Riccati equation. The non-commutative Riccati equation is solved and hence suitable conserved quantities are derived. In this context we also discuss the infinite dimensional case of the NLS matrix model as it provides a suitable candidate for a quantum version of the usual NLS model. Similarly, the non-commutitave Riccati equation for the general dressing transform is derived and it is naturally equivalent to the one emerging from the solution of the auxiliary linear problem. Comment: 29 pages, LaTex. Minor modifications |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1016/j.nuclphysb.2019.02.019 |
| URL الوصول: | http://arxiv.org/abs/1810.10937 |
| رقم الأكسشن: | edsarx.1810.10937 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1016/j.nuclphysb.2019.02.019 |
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