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Zbl 1203.35059
Ma, Wen-Xiu; Wu, Hongyou; He, Jingsong
Partial differential equations possessing Frobenius integrable decompositions. (English)
[J] Phys. Lett., A 364, No. 1, 29-32 (2007). ISSN 0375-9601

Summary: Frobenius integrable decompositions are introduced for partial differential equations. A procedure is provided for determining a class of partial differential equations of polynomial type, which possess specified Frobenius integrable decompositions. Two concrete examples with logarithmic derivative Bäcklund transformations are given, and the presented partial differential equations are transformed into Frobenius integrable ordinary differential equations with cubic nonlinearity. The resulting solutions are illustrated to describe the solution phenomena shared with the KdV and potential KdV equations.

MSC 2000:: *35C05 Solutions of PDE in closed form
35Q53 KdV-like equations
37K10 Completely integrable systems etc.
35A30 Geometric theory for PDE, transformations

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