Families of rational solition solution of the Kadomisev-Petviashvili I equation

Year: 2016

Authors: Chen SH., Grelu P., Mihalache D., Baronio F.

Autors Affiliation: Southeast Univ, Dept Phys, Nanjing 211189, Jiangsu, Peoples R China;‎ Univ Bourgogne Franche Comte, UMR CNRS 6303, Lab ICB, 9 Ave A Savary, F-21078 Dijon, France; Horia Hulubei Natl Inst Phys & Nucl Engn, Dept Theoret Phys, RO-077125 Bucharest, Romania; Univ Brescia, INO CNR, Via Branze 38, I-25123 Brescia, Italy; Univ Brescia, Dipartimento Ingn Informaz, Via Branze 38, I-25123 Brescia, Italy

Abstract: Families of exact explicit nonsingular rational soliton (lump) solutions of any order to the Kadomtsev-Petviashvili I equation are presented in a compact form. We show that the higher-order lump solutions may exhibit rich patterns on a finite background, but invariably evolve from a vertical distribution at large negative time into a horizontal distribution at large positive time, within an appropriate Galilean transformed frame. A universal polynomial equation is then put forward, whose real roots can accurately determine the lump positions in such a complex multi-lump distribution. We also unveil that there is an intimate relation between certain lump structures and the rogue-wave hierarchy. We expect that this finding may provide a new pathway for understanding the higher-dimensional rogue waves.

Journal/Review: ROMANIAN REPORTS IN PHYSICS

Volume: 68 (4)      Pages from: 1407  to: 1424

KeyWords: Rational soliton; rogue wave; Kadomtsev-Petviashvili equation

Citations: 47
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