Multiparametric families of solutions of the Kadomtsev-Petviashvili-I equation, the structure of their rational representations, and multi-rogue waves

DOI10.1134/S0040577918080068zbMath1402.35067OpenAlexW2891202048MaRDI QIDQ1626667

Pierre Gaillard

Publication date: 21 November 2018

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0040577918080068

zbMATH Keywords

WronskianFredholm determinantKadomtsev-Petviashvili equationrogue wavelump

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Soliton solutions (35C08)

Related Items (5)

Classification of KPI lumps ⋮ Pattern transformation in higher-order lumps of the Kadomtsev-Petviashvili I equation ⋮ Multi-lump wave patterns of KPI via integer partitions ⋮ Universal rogue wave patterns associated with the Yablonskii-Vorob'ev polynomial hierarchy ⋮ Families of solutions to the KPI equation given by an extended Darboux transformation

Cites Work

• Unnamed Item
• Unnamed Item
• Rational solutions to the KPI equation and multi rogue waves
• Darboux transformation and explicit solutions of the Kadomtsev-Petviashvili equation, depending on functional parameters
• Elliptic solutions of the Kadomtsev-Petviashvili equation and integrable systems of particles
• Holomorphic bundles over Riemann surfaces and the Kadomtsev-Petviashvili equation. I
• Rational solutions of the Kadomtsev-Petviashvili equation and integrable systems of \(n\) particles on a line
• A novel class of solutions of the non-stationary Schrödinger and the Kadomtsev-Petviashvili I equations
• On the discrete spectrum of the nonstationary Schrödinger equation and multipole lumps of the Kadomtsev-Petviashvili I equation
• On the evolution of packets of water waves
• Fredholm and Wronskian representations of solutions to the KPI equation and multi-rogue waves
• The use of Backlund transformations in obtaining N-soliton solutions in Wronskian form
• Two-dimensional lumps in nonlinear dispersive systems
• Rational solutions of the Kadomtsev–Petviashvili hierarchy and the dynamics of their poles. I. New form of a general rational solution
• On a family of solutions of the Kadomtsev–Petviashvili equation which also satisfy the Toda lattice hierarchy
• Solutions to the Time Dependent Schrödinger and the Kadomtsev-Petviashvili Equations
• Young diagrams and N-soliton solutions of the KP equation

This page was built for publication: Multiparametric families of solutions of the Kadomtsev-Petviashvili-I equation, the structure of their rational representations, and multi-rogue waves