31 citations · 91 across the 14 of their papers we have counts for
15 papers
A Classification of Hirota-Integrable Supersymmetric Bilinear KdV-Type Equations
Laurent Delisle, Amine Jaouadi
We present a classification of supersymmetric bilinear KdV-type equations admitting unconstrained three-super-soliton solutions. Extending Hirota's classical three-soliton criterio…
Vector Representation of Exact Soliton Dynamics in Multi-component Nonlinear Schrödinger Systems
Maxime Foucher, Laurent Delisle, Amine Jaouadi
Multicomponent nonlinear Schrödinger equations constitute fundamental models for coherent matter waves in multicomponent Bose--Einstein condensates, spinor quantum fluids, and vect…
A Vector Bilinear Framework for Soliton Dynamics in Coupled Modified KdV Systems
Laurent Delisle, Amine Jaouadi
We investigate the integrable structure and soliton dynamics of a coupled modified Korteweg-de Vries (cmKdV) system with a real symmetric coupling matrix. We introduce a vector ref…
A novel Hirota bilinear approach to supersymmetric equations
Laurent Delisle
This article presents a novel application of the Hirota bilinear formalism to the supersymmetric KdV and Burgers equations. This new approach avoids splitting N=2 equations i…
A N=2 extension of the Hirota bilinear formalism and the supersymmetric KdV equation
Laurent Delisle
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, hie…
Superforms and the supersymmetric sigma model
Laurent Delisle
We present a characterisation of Maurer-Cartan 1-superforms associated to the two-dimensional supersymmetric sigma model. We, then, solve the associated linear…
General solutions of the supersymmetric sigma model and its generalisation to
Laurent Delisle, Véronique Hussin, Wojtek J. Zakrzewski
A new approach for the construction of finite action solutions of the supersymmetric sigma model is presented. We show that this approach produces more non-holo…
Geometry of surfaces associated to grassmannian sigma models
Laurent Delisle, Véronique Hussin, Wojtek J. Zakrzewski
We investigate the geometric characteristics of constant gaussian curvature surfaces obtained from solutions of the sigma model. Most of these solutions are related to the…
Constant curvature surfaces of the supersymmetric sigma model
Laurent Delisle, Véronique Hussin, İsmeth Yurduşen +1
Constant curvature surfaces are constructed from the finite action solutions of the supersymmetric sigma model. It is shown that there is a unique holomorphic s…
Classical and SUSY solutions of the Boiti-Leon-Manna-Pempinelli equation
Laurent Delisle, Masoud Mosaddeghi
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…
Constant curvature solutions of Grassmannian sigma models: (2) Non-holomorphic solutions
Laurent Delisle, Véronique Hussin, Wojtek J. Zakrzewski
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 whic…
Soliton and similarity solutions of N=2,4 supersymmetric equations
Laurent Delisle, Véronique Hussin
We produce soliton and similarity solutions of supersymmetric extensions of Burgers, Korteweg-de Vries and modified KdV equations. We give new representations of the -functions…
Constant curvature solutions of Grassmannian sigma models: (1) Holomorphic solutions
Laurent Delisle, Veronique Hussin, Wojtek J. Zakrzewski
We present a general formula for the Gaussian curvature of curved holomorphic 2-spheres in Grassmannian manifolds G(m, n). We then show how to construct such solutions with constan…
New solution of the Supersymmetric KdV equation via Hirota methods
Laurent Delisle, Véronique Hussin
We consider the resolution of the supersymmetric KdV equation with () from the Hirota formalism. For the first time, a bilinear form of the $SKd…
Links between symmetry reduction and Hirota methods of the N=2 susy KdV equation
Laurent Delisle, Véronique Hussin
We consider the resolution of the N=2 supersymmetric KdV equation with a=-2 (SKdV_{a=-2}) from two approaches, the group invariant method (or symmetry reduction) and the Hirota for…