We consider the negative order KdV (NKdV) hierarchy which generates nonlinear integrable equations. Selecting different seed functions produces different evolution equations. We apply the traveling wave setting to study one of these equations. Assuming a particular type of solution leads us to solve a cubic equation. New solutions are found, but none of these are classical solitary traveling wave solutions.
Rodriguez M, Li J, Qiao Z. Negative Order KdV Equation with No Solitary Traveling Waves. Mathematics. 2022; 10(1):48. https://doi.org/10.3390/math10010048
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