\(N=2\) super \(W_3\) algebra and \(N=2\) super Boussinesq equations

DOI10.1142/S0217751X95000127zbMATH Open0985.81534arXivhep-th/9305070MaRDI QIDQ2775381

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Publication date: 26 February 2002

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Abstract: We study classical $N=2$ super-$W_3$ algebra and its interplay with $N=2$ supersymmetric extensions of the Boussinesq equation in the framework of the nonlinear realization method and the inverse Higgs - covariant reduction approach. These techniques have been previously applied by us in the bosonic $W_3$ case to give a new geometric interpretation of the Boussinesq hierarchy. Here we deduce the most general $N=2$ super Boussinesq equation and two kinds of the modified $N=2$ super Boussinesq equations, as well as the super Miura maps relating these systems to each other, by applying the covariant reduction to certain coset manifolds of linear $N=2$ super-$W_3^{infty}$ symmetry associated with $N=2$ super-$W_3$. We discuss the integrability properties of the equations obtained and their correspondence with the formulation based on the notion of the second hamiltonian structure.

Full work available at URL: https://arxiv.org/abs/hep-th/9305070

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