Abstract
Starting from an improved projective method and a linear variableseparation approach, new families of variable separation solutions(including solitary wave solutions, periodic wave solutions andrational function solutions) with arbitrary functions for the(2+1)-dimensional generalized Broer–Kaup (GBK) system are derived.Usually, in terms of solitary wave solutions and/or rationalfunction solutions, one can find abundant important localizedexcitations. However, based on the derived periodic wave solutionin this paper, we reveal some complex wave excitations in the(2+1)-dimensional GBK system, which describe solitons moving on aperiodic wave background. Some interestingevolutional properties for these solitary waves propagating onthe periodic wave background are also briefly discussed.
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