Abstract
In this Letter, the multi-linear variable separation approach which is based on corresponding Bäcklund transformation (MLVSA-BT) is extended to solve a ( 1 + 1 ) -dimensional third-order nonlinear evolution equation and a ( 1 + 1 ) -dimensional differential-difference Toda-like equation. New exact solution with an arbitrary function is derived. Abundant coherent structures such as soliton and solitoff can be found by selecting corresponding lower-dimensional function appropriately.
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