Rational solutions of the KP hierarchy and the dynamics of their poles. II. Construction of the degenerate polynomial solutions

DOI10.1063/1.532577zbMath0927.37048OpenAlexW2063527260MaRDI QIDQ4701490

Dmitry E. Pelinovsky

Publication date: 21 November 1999

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/061f0bda1fe71396c0b300c49d9788d7e1fa04e6

zbMATH Keywords

Boussinesq equationpolynomial solutions\(\tau\)-functionsKadomtsev-Petviashvili hierarchyscattering dynamicsGardner equations

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53)

Related Items (18)

Dynamics of KPI lumps ⋮ Classification of KPI lumps ⋮ Resonant collisions between lumps and periodic solitons in the Kadomtsev–Petviashvili I equation ⋮ Pattern transformation in higher-order lumps of the Kadomtsev-Petviashvili I equation ⋮ Special polynomials associated with rational solutions of the Painlevé equations and applications to soliton equations ⋮ Kadomtsev-Petviashvili equation: one-constraint method and lump pattern ⋮ Multi-lump wave patterns of KPI via integer partitions ⋮ Construction of rational solutions of the real modified Korteweg-de Vries equation from its periodic solutions ⋮ General soliton solution to a nonlocal nonlinear Schrödinger equation with zero and nonzero boundary conditions ⋮ Remarks on the solutions of the Kadomtsev-Petviashvili equation ⋮ A novel class of solutions of the non-stationary Schrödinger and the Kadomtsev-Petviashvili I equations ⋮ Rational solutions of the classical Boussinesq system ⋮ Nonlinear wave transitions and their mechanisms of (2+1)-dimensional Sawada-Kotera equation ⋮ Universal rogue wave patterns associated with the Yablonskii-Vorob'ev polynomial hierarchy ⋮ Nondegeneracy, Morse index and orbital stability of the KP-I lump solution ⋮ Generation mechanism of high-order rogue waves via the improved long-wave limit method: NLS case ⋮ RATIONAL SOLUTIONS OF THE BOUSSINESQ EQUATION ⋮ An extended noncommutative KP hierarchy

Cites Work

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