Nonlinear Dynamics

, Volume 95, Issue 2, pp 1133–1146 | Cite as

Rational and semi-rational solutions of the Kadomtsev–Petviashvili-based system

  • Yongshuai Zhang
  • Jiguang Rao
  • K. Porsezian
  • Jingsong HeEmail author
Original Paper


We investigate the rational and semi-rational solutions of the integrable Kadomtsev–Petviashvili (KP)-based system, which appears in fluid mechanics, plasma physics, and gas dynamics. Various types of solutions, including soliton, breather, and a mixture of breather and soliton, of the KP-based system are derived by applying the Hirota’s bilinear method and the perturbation expansion. By taking a long-wave limit of the soliton solutions and particular parameter constraints, the rational and semi-rational solutions are generated. The rational solutions have two different dynamical behaviors: lump and line rogue wave; the first-order lump and line rogue wave are classified into three patterns: bright state, mixed state, and dark state. The semi-rational solutions reveal the following dynamic features: (1) Elastic interactions between lumps and bound-state dark solitons; (2) Elastic interactions between line rogue waves and bound-state dark solitons; (3) Inelastic collisions of breathers and rogue waves. Compared to the rational solutions, the semi-rational solutions have more interesting patterns.


Kadomtsev–Petviashvili-based system Rogue wave solution Bilinear method Semi-rational solution 



This work is supported by the NSF of China under Grant Nos. 11671219, 11801510 and the K.C. Wong Magna Fund in Ningbo University. K. Porsezian acknowledges DST-SERB, NBHM, IFCPAR and CSIR, the Government of India, for financial support through major projects.

Compliance with ethical standards

Conflict of interest

We declare we have no conflict of interests.


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.College of ScienceZhejiang University of Science and TechnologyHangzhouPeople’s Republic of China
  2. 2.School of Mathematical SciencesUniversity of Science and Technology of ChinaHefeiPeople’s Republic of China
  3. 3.Department of PhysicsPondicherry UniversityKalapetIndia
  4. 4.Department of MathematicsNingbo UniversityNingboPeople’s Republic of China

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