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pro vyhledávání: '"Delisle, Laurent"'
This study investigates the formation and dynamics of solitons in Bose-Einstein condensates (BECs) within dark traps generated by two crossed Laguerre-Gaussian (LG) beams with varying azimuthal indices $\ell$. As the index $\ell$ increases, the poten
Externí odkaz:
http://arxiv.org/abs/2412.07574
Autor:
Delisle, Laurent
Publikováno v:
J. Phys. A: Math. Theor. 56 455202 (2023)
This article presents a novel application of the Hirota bilinear formalism to the $N=2$ supersymmetric KdV and Burgers equations. This new approach avoids splitting N=2 equations into two $N=1$ equations. We use the super Bell polynomials to obtain b
Externí odkaz:
http://arxiv.org/abs/2306.05220
Autor:
Delisle, Laurent
We present a bilinear Hirota representation of the N=2 supersymmetric extension of the Korteweg-de Vries equation. This representation is deduced using binary Bell polynomials, hierarchies and fermionic limits. We, also, propose a new approach for th
Externí odkaz:
http://arxiv.org/abs/1509.03137
Autor:
Delisle, Laurent
We present a characterisation of Maurer-Cartan 1-superforms associated to the two-dimensional supersymmetric $\mathbb{C}P^{N-1}$ sigma model. We, then, solve the associated linear spectral problem and use its solutions to describe an integrable syste
Externí odkaz:
http://arxiv.org/abs/1508.06748
A new approach for the construction of finite action solutions of the supersymmetric $\mathbb{C}P^{N-1}$ sigma model is presented. We show that this approach produces more non-holomorphic solutions than those obtained in previous approaches. We study
Externí odkaz:
http://arxiv.org/abs/1507.08508
We investigate the geometric characteristics of constant gaussian curvature surfaces obtained from solutions of the $G(m,n)$ sigma model. Most of these solutions are related to the Veronese sequence. We show that we can distinguish surfaces with the
Externí odkaz:
http://arxiv.org/abs/1412.1368
Publikováno v:
J. Math. Phys. 56, 023506 (2015)
Constant curvature surfaces are constructed from the finite action solutions of the supersymmetric $\mathbb{C}P^{N-1}$ sigma model. It is shown that there is a unique holomorphic solution which leads to constant curvature surfaces: the generalized Ve
Externí odkaz:
http://arxiv.org/abs/1406.3371
Autor:
Delisle, Laurent, Mosaddeghi, Masoud
Publikováno v:
J. Phys. A: Math. Theor. 46 (2013) 115203
In this paper, we propose the study of the Boiti-Leon-Manna-Pempinelli equation from two point of views: the classical and supersymmetric cases. In the classical case, we construct new solutions of this equation from Wronskian formalism and Hirota me
Externí odkaz:
http://arxiv.org/abs/1211.1165
We generalize here our general procedure for constructing constant curvature maps of 2-spheres into Grassmannian manifolds G(m,n) this time concentrating our attention on maps which are non-holomorphic. We present some expressions describing these so
Externí odkaz:
http://arxiv.org/abs/1210.5864
Autor:
Delisle, Laurent, Hussin, Véronique
Publikováno v:
Symmetry. 2012; 4(3):441-451
We produce soliton and similarity solutions of supersymmetric extensions of Burgers, Korteweg-de Vries and modified KdV equations. We give new representations of the $\tau$-functions in Hirota bilinear formalism. Chiral superfields are used to obtain
Externí odkaz:
http://arxiv.org/abs/1205.5593