Z. Naturforsch. 68a, 735 – 743
Elastic and Inelastic Interaction Behaviours for the (2 + 1)-Dimensional Nizhnik–Novikov–Veselov Equation in Water Waves
School of Sciences, Zhejiang Agriculture and Forestry University, Lin'an, Zhejiang 311300, P.R. China
Received June 12, 2013 / published online October 16, 2013
A modified mapping method and new ansätz form are used to derive three families of variable separation solutions with two arbitrary functions of the (2 + 1)-dimensional Nizhnik–Novikov–Veselov equation in water waves. By selecting appropriate functions in the variable separation solution, we discuss interaction behaviours among dromion-pair and dromion-like peakon-pair and dromion-like semifoldon-pair. The analysis results exhibit that the interaction behaviours between dromion-pair and dromion-like peakon-pair, dromion-pair and semifoldon-pair, dromion-like peakon-pair and semifoldon-pair are all incomplete elastic, and there exists a phase shift. The interaction behaviour between two dromion-like semifoldon-pairs is completely elastic, and no phase shift appears after interaction. Moreover, during the interactions between dromion-pair and semifoldon-pair, dromion-like peakon-pair and
semifoldon-pair, and between two dromion-like semifoldon-pairs, there all exist a multi-valued semifoldon-pair.
Key words: Modified Mapping Method; Nizhnik–Novikov–Veselov Equation; Elastic and Inelastic Interaction.
PACS numbers: 05.45.Yv; 02.30.Ik; 03.65.Ge