Generation of anomalously scattered lumps via lump chains degeneration within the Mel’nikov equation

This paper explores two distinct approaches for degenerating lump chains into anomalously scattered lumps within the Mel’nikov equation. The first approach involves directly degenerating lump chains with specific phase parameters by simultaneously modulating their periods. The second approach entails equalizing the parameters of distinct lump chains to obtain a degenerate lump chain, followed by adjusting its period to infinity to achieve anomalously scattered lumps. We also calculate the asymptotic form of the degenerate lump chains at large time and establishes the relationship between peak locations of the anomalously scattered lumps and certain polynomials.