Elastic interactions between multi-valued foldons and anti-foldons for the (2+1)-dimensional variable coefficient Broer-Kaup system in water waves

With the help of the improved tanh-function method, some exact variable separation solutions for a (2+1)-dimensional variable coefficient Broer-Kaup system in water waves are found. The detailed investigation indicates that these seemly independent variable separation solutions actually depend on each other. Based on the exact variable separation solution, completely and noncompletely elastic interactions between multi-valued foldons and anti-foldons are studied analytically and graphically.