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Bilinear approach to \(N = 2\) supersymmetric KdV equations. (English) Zbl 1179.35301

Summary: The \(N = 2\) supersymmetric KdV equations are studied within the framework of the Hirota bilinear method. For two such equations, namely \(N = 2\), \(a = 4\) and \(N = 2\), \(a = 1\) supersymmetric KdV equations, we obtain the corresponding bilinear formulations. Using them, we construct particular solutions for both cases. In particular, a bilinear Bäcklund transformation is given for the \(N = 2\), \(a = 1\) supersymmetric KdV equation.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
35Q51 Soliton equations
35C05 Solutions to PDEs in closed form
35C08 Soliton solutions

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