Question: How determine interval of singularity in complex function?

in a lot of my function i have a interval which is make my function singular and i don't know how remove this singularity even when i am change a lot of parameter with explore which explore option for plot is a little bit heavy for more than  7 or 8 parameter for running , and i know the shape of the graph is 2-soliton and 1-breather(zig-zag) but i have to see the shape and make my plot have a best shape  there is any idea for fixing this issue?

singular-interval.mw

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