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

More Information: This work was supported by the National Natural Science Foundation of China (Grants No. 11174050 and No. 11474051), by the Italian Ministry of University and Research (MIUR, Project No. 2012BFNWZ2), and by CEFIPRA/IFCPAR under Project 5104-2.
KeyWords: Rational soliton; rogue wave; Kadomtsev-Petviashvili equation

Citations: 52
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