Derivation of weakly interacting lumps for the (2+1)-dimensional Yu–Toda–Sasa–Fukuyama equation via degeneracy of lump chains

Abstract

This paper introduces two distinct pathways for degenerating normally interacting lump chains into weakly interacting lump waves for Yu–Toda–Sasa–Fukuyama equation, which will enrich the correlation between lump chains and weakly interacting lump waves. The first pathway involves letting the periods of $M$ similarly-velocity lump chains approach infinity directly. The second pathway first transforms $M$ normally interacting lump chains into weakly interacting lump chains with similar dynamic behaviors. Then, by allowing their periods to approach infinity, $\frac{M\left(M+1\right)}{2}$ weakly interacting lump waves are produced. Distance between weakly interacting lump chains in this equation is proportional to $ln\left|t\right|$, while between weakly interacting lump waves is proportional to $\sqrt[3]{\left|t\right|}$. These findings will contribute valuable theoretical insights to the study of wave theory, ocean science and related disciplines.