Some algebro-geometric solutions for the coupled modified Kadomtsev-Petviashvili equations arising from the Neumann type systems

DOI10.1063/1.4736838zbMath1288.35417OpenAlexW2010827782MaRDI QIDQ2865519

Jinbing Chen

Publication date: 29 November 2013

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

Full work available at URL: https://doi.org/10.1063/1.4736838

zbMATH Keywords

algebro-geometric solutionsintegrable nonlinear evolution equationscoupled modified Kadomtsev-Petviashvili equationsNeumann type systems

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) Elliptic curves (14H52) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) 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)

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Darboux transformation and novel solitons of a coupled system, Trigonal curves and algebro-geometric solutions to soliton hierarchies I

Cites Work

• Separation of variables in the classical integrable \(\mathrm{SL}(3)\) magnetic chain
• The periodic problem for the Korteweg-de Vries equation
• A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I
• Hill's operator with finitely many gaps
• The spectrum of Hill's equation
• Periodic problems for the Korteweg-de Vries equation in the class of finite band potentials
• The \(r\)-matrix and an algebraic-geometric solution of the AKNS system
• New integrable hierarchies from vertex operator representations of polynomial Lie algebras
• Algebro-geometric solutions of (2+1)-dimensional coupled modified Kadomtsev–Petviashvili equations
• Exact Solution of the Korteweg—de Vries Equation for Multiple Collisions of Solitons
• Neumann type integrable reduction for nonlinear evolution equations in 1+1 and 2+1 dimensions
• The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems
• Periodic solutions of the KdV equation
• NON-LINEAR EQUATIONS OF KORTEWEG-DE VRIES TYPE, FINITE-ZONE LINEAR OPERATORS, AND ABELIAN VARIETIES
• Lax representation, r-matrix method, and separation of variables for the Neumann-type restricted flow
• Relation between the Kadometsev–Petviashvili equation and the confocal involutive system
• The finite-band solution of the Jaulent–Miodek equation
• Quasi-periodic solutions of the modified Kadomtsev-Petviashvili equation
• Finite-gap solutions of 2+1 dimensional integrable nonlinear evolution equations generated by the Neumann systems
• Integrals of nonlinear equations of evolution and solitary waves
• C Neumann and Bargmann systems associated with the coupled KdV soliton hierarchy
• Tata lectures on theta. II: Jacobian theta functions and differential equations. With the collaboration of C. Musili, M. Nori, E. Previato, M. Stillman, and H. Umemura
• The complex geometry of weak piecewise smooth solutions of integrable nonlinear PDE's of shallow water and Dym type