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Bilinearization of \(N=1\) supersymmetric Korteweg-de Vries equation revisited. (English) Zbl 1080.35122

Summary: We consider the \(N=1\) supersymmetric Korteweg-de Vries (sKdV) equation within the framework of Hirota’s bilinear method. We construct a Bäcklund transformation which may be interpreted as the modified sKdV equation. Also, we find a Lax representation and a nonlinear superposition formula. By direct applications of the nonlinear superposition formula, we calculate soliton solutions for the sKdV equation.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
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