Abstract
In the literature, there have been considerable interests in the study of nonsingular rational solutions for nonlinear integrable models. These nonsingular rational solutions have appeared with different names in a variety of nonlinear systems, say, algebraic solitons, algebraic solitrary waves and lump solutions etc. More importantly, these nonsingular rational solutions have played a key role in the study of rogue waves. In the paper, we will develop a new procedure to generate lump solutions via Bäcklund transformations and nonlinear superposition formulae for some integrable models. It is shown that our procedure can be utilized to some well-studied equations such as KPI equation, elliptic Toda equation and BKP equation, but also to comparatively less-studied DJKM equation, Novikov-Veselov equation and negative flow of the BKP equation.
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