KP, perturbed line soliton

 

For ε = 1, the KP equation has solitonic solutions which are localized in both spatial directions with an algebraic fall off. These solutions are called lump solitons. In this case the line solitons are unstable and will form lump solitons if perturbed, see 124/2005 and references therein. The video shows a perturbed KdV soliton where the perturbations grow up to the formation of lump solitons.

C. Klein, C. Sparber and P. Markowich