Nonlinear superposition between lump and other waves of the (2+1)-dimensional generalized Caudrey-Dodd-Gibbon-Kotera-Sawada equation in fluid dynamics

With the premise that N-soliton solutions are acquired, this paper will focus on the nonlinear superposition between one lump and other types of localised waves of the (2+1)-dimensional generalized Caudrey-Dodd-Gibbon-Kotera-Sawada(gCDGKS) equation. By introducing a novel constraint, combining the long wave limit method and mode resonance method, it is guaranteed that there is no interaction between one lump (local waves that remain wave form invariant in space) and line solitons (analytic solutions in exponential form in both space and time), breather waves and resonant Y-type solitons ever or that one lump is always situated on at least one of line solitons, breather waves (shape is similar to the rise and fall of the breath) and resonant Y-type solitons (similar to the letter Y in spatial structure). In addition, by defining novel velocity resonance constraints, it is ensured that lump and line waves, lump and breather waves, breather and line wave have exactly the same velocity magnitude and direction, which means that they form new molecularly bound states. Remarkably, we find that one line and one breather wave can be transformed into two breather waves. In general, lump wave interact with other types of localised waves in three stages: before, during and after the interaction, but the results obtained in this paper break this perception and provide some references for the explanation of certain nonlinear phenomena occurring in fields such as shallow water waves, solitons and fluid mechanics.

Automated summary

By introducing a novel constraint, this paper investigates the nonlinear superposition between one lump and other types of localised waves in the (2+1)-dimensional generalized Caudrey-Dodd-Gibbon-Kotera-Sawada (gCDGKS) equation. The results show that there is no interaction between the lump wave and line solitons, breather waves, and resonant Y-type solitons. Furthermore, the study defines novel velocity resonance constraints, ensuring that different types of localised waves have the same velocity magnitude and direction. This research provides important references for understanding certain nonlinear phenomena in fields such as shallow water waves, solitons, and fluid mechanics.