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Nonlinear Schrödinger equations and \(N = 1\) superconformal algebra. (English) Zbl 1138.37329
From the introduction: In this paper, we obtain super-extensions of coupled NLS equations using \(N = 1\) superconformal algebra with Neveu-Schwarz and Ramond types. In Section 2, we discuss the osp\((1,2)\) superalgebra valued soliton connection and we obtain coupled super NLS equations. Sections 3 and 4 concern the soliton connection for the \(N=1\) superconformal algebra with Neveu-Schwarz type and Ramond type, respectively and we will obtain in these sections two different types of super-extensions of coupled NLS equations.

MSC:
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
17B80 Applications of Lie algebras and superalgebras to integrable systems
35Q55 NLS equations (nonlinear Schrödinger equations)
37K30 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures
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References:
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