Partial differential equations possessing Frobenius integrable decompositions
نویسندگان
چکیده
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. © 2006 Elsevier B.V. All rights reserved. PACS: 05.45.-a; 02.30.Ik
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