An N=1 supersymmetric generalization of coupled dispersionless (SUSY-CD) integrable system has been proposed by writing its superfield Lax representation. It has been shown that under a suitable variable transformation, the SUSY-CD integrable system is equivalent to N=1 supersymmetric sine-Gordon equation. A superfield bilinear form of SUSY-CD integrable system has been proposed by using super Hirota operator. Explicit expressions of superfield soliton solutions of SUSY-CD integrable system have been obtained by using the Hirota method.

Abstract. A bilinear form of KdV and SUSY KdV equations has been studied in the framework of Hirota method. The properties of Hirota operator have been proved. We have expressed simplified version of Hirota method for KdV equation. The rational solutions of KdV equation have been reviewed, and we obtain the rational solutions of SUSY KdV equation.

Исследовано суперсимметричное расширение уравнения Пенлеве II, предложены его суперполевая билинейная форма, а также иерархия суперсимметричного уравнения Пенлеве II.

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