Abstract
By means of an new auxiliary equation method based on mapping method and the second-order linear ordinary differential equation, some types of variable separation solutions with two arbitrary lower dimensional functions of the 2+1 dimensional Ablowitz–Kaup–Newell–Segur system are derived. Based on the derived variable separation excitation, some new special types of non-localized solutions such as doubly periodic wave and line periodic wave are constructed by choosing appropriate functions. In addition, we also investigate the annihilation phenomenon and non-elastic interaction graphically.
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