Abstract
The (2+1)-dimensional Eckhaus-type extension of the dispersive long wave (EEDLW) equation is investigated, which was obtained in the appropriate approximation from the basic equations of hydrodynamics. Though it has no Painleve property, we gain an auto-Backlund transformation (aBT) by truncating the Laurent series expansion at O(w0). In particular, the special one of the aBT establishes a relationship between the EEDLW equation and a set of three linear partial differential equations involving the well-known heat equation. Finally many types of new exact solutions of the EEDLW equation are found from the obtained aBT and some proper ansatze, which may be useful to explain some physical phenomena.
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