Algebro-geometric solutions of (2+1)-dimensional coupled modified Kadomtsev–Petviashvili equations

DOI10.1063/1.533134zbMath0991.37045OpenAlexW2068431239MaRDI QIDQ2737823

Hui-Hui Dai, Xiangguo Geng

Publication date: 30 August 2001

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

Full work available at URL: https://doi.org/10.1063/1.533134

zbMATH Keywords

modified Kadomtsev-Petviashvili equation

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) Relationships between algebraic curves and integrable systems (14H70) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20)

Related Items (12)

Darboux transformation and novel solitons of a coupled system ⋮ A generalized Zakharov-Shabat equation with finite-band solutions and a soliton-equation hierarchy with an arbitrary parameter ⋮ Algebro-geometric solutions of a \((2+1)\)-dimensional integrable equation associated with the Ablowitz-Kaup-Newell-Segur soliton hierarchy ⋮ Decomposition of a \(2 + 1\)-dimensional Volterra type lattice and its quasi-periodic solutions ⋮ Generations of integrable hierarchies and exact solutions of related evolution equations with variable coefficients ⋮ On the decomposition of the modified Kadomtsev–Petviashvili equation and explicit solutions ⋮ A two-component generalization of Burgers' equation with quasi-periodic solution ⋮ A few new higher-dimensional Lie algebras and two types of coupling integrable couplings of the AKNS hierarchy and the KN hierarchy ⋮ Coupling integrable couplings and bi-Hamiltonian structure associated with the Boiti–Pempinelli–Tu hierarchy ⋮ Some algebro-geometric solutions for the coupled modified Kadomtsev-Petviashvili equations arising from the Neumann type systems ⋮ An integrable system and associated integrable models as well as Hamiltonian structures ⋮ Binary nonlinearization of spectral problems of the perturbation AKNS systems.

Cites Work

• Real finite-gap regular solutions of the Kaup-Boussinesq equation
• Inverse problem for periodic finite-zoned potentials in the theory of scattering
• An Alternative Approach to Algebro-Geometric Solutions of the AKNS Hierarchy
• Finite-band solutions of the classical Boussinesq–Burgers equations
• Quasi-periodic solutions of the modified Kadomtsev-Petviashvili equation
• C Neumann and Bargmann systems associated with the coupled KdV soliton hierarchy

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