Bilinear Approach to Supersymmetric KdV Equation
نویسندگان
چکیده
منابع مشابه
Bilinear Approach to Supersymmetric KdV Equation
Extending the gauge-invariance principle for τ functions of the standard bilinear formalism to the supersymmetric case, we define N = 1 supersymmetric Hirota operators. Using them, we bilinearize SUSY KdV equation. The solution for multiple collisions of super-solitons is given.
متن کاملExtension of the bilinear formalism to supersymmetric KdV-type equations
Extending the gauge-invariance principle for τ functions of the standard bilinear formalism to the supersymmetric case, we define N=1 supersymmetric Hirota operators. Using them, we bilinearize SUSY KdV-type equations (KdV, Sawada-Kotera-Ramani, Hirota-Satsuma). The solutions for multiple collisions of super-solitons and extension to SUSY sine-Gordon are also discussed.
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The N = 2 supersymmetric KdV equations are studied within the framework of Hirota’s 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 supersymmetr...
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u(x, 0) = u0(x), where u0 ∈ H(R). Our principal aim here is to lower the best index s for which one has local well posedness in H(R), i.e. existence, uniqueness, persistence and continuous dependence on the data, for a finite time interval, whose size depends on ‖u0‖Hs . Equation in (1.1) was derived by Korteweg and de Vries [21] as a model for long wave propagating in a channel. A large amount...
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ژورنال
عنوان ژورنال: Journal of Non-linear Mathematical Physics
سال: 2001
ISSN: 1402-9251
DOI: 10.2991/jnmp.2001.8.supplement.9