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A modified mapping method is used to obtain variable separation solution with two arbitrary functions of the (2+1)-dimensional Broer-Kaup-Kupershmidt equation. Based on the variable separation solution and by selecting appropriate functions, we discuss the completely elastic head-on collision between two dromion-lattices, non-completely elastic "chase and collision" between two multi-dromion-pairs and completely non-elastic interaction phenomenon between anti-dromion and dromion-pair.

We reduce the variable-coefficient higher-order nonlinear Schrödinger equation (VCHNLSE) into the constant-coefficient (CC) one. Based on the reduction transformation and solutions of CCHNLSE, we obtain analytical soliton solutions embedded in the continuous wave background for the VCHNLSE. Then the excitation in advancement and sustainment of soliton arrays, and postponed disappearance and sustainment of the bright soliton embedded in the background are discussed in an exponential system.

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