Rogue wave and a pair of resonance stripe solitons to a reduced generalized (3+1)-dimensional KP equation

TL;DR

This paper derives lump solutions and explores rogue wave phenomena in a reduced (3+1)-dimensional KP equation, revealing interactions between solitons and the formation of rogue waves through analytical and graphical methods.

Contribution

It introduces new lump solutions with six parameters and demonstrates rogue wave formation from interactions with resonance stripe solitons in a (3+1)-dimensional KP model.

Findings

Lump solutions are rationally localized in all directions.

Interaction with stripe solitons can drown lump solitons.

Rogue waves can be generated by resonance soliton interactions.

Abstract

Based on the bilinear operator and symbol calculation, some lump solutions are presented, rationally localized in all directions in the space, to a reduced (3+1)-dimensional KP equation. The lump solutions all contain six parameters, four of which must cater to the non-zero conditions so as to insure the analyticity and rational localization, while the others are free. Then the interaction between lump soliton and one stripe soliton is described and the result shows that the lump soliton will be drowned or swallowed by the stripe soliton. Furthermore, we extend this method to a new combination of positive quadratic function and hyperbolic functions. Especially, it is interesting that a rogue wave is found to be aroused by the interaction between lump soliton and a pair of resonance stripe solitons. By choosing the values of the parameters, the dynamic properties of lump solution, interaction between lump soliton and one stripe soliton, rogue wave, generated by the interaction between lump soliton and a pair of resonance solitons, are shown graphically.