Computer-algebra methods for investigation of hereditary operators of higher order soliton equations

DOI10.1016/0010-4655(87)90015-4zbMath0664.65118OpenAlexW2165725388MaRDI QIDQ1115545

Benno Fuchssteiner, Waldemar Wiwianka, Walter Oevel

Publication date: 1987

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0010-4655(87)90015-4

zbMATH Keywords

computer algebrarecursion operatorsMAPLEsoliton equationscoupled systemsMACSYMA5th order nonlinear partial differential equationshereditary operators

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Partial differential equations of mathematical physics and other areas of application (35Q99) Applications to the sciences (65Z05)

Related Items

On the Recursion Operator for the Noncommutative Burgers Hierarchy, Analytical solutions for some nonlinear evolution equations, Mastersymmetries, angle variables, and recursion operator of the relativistic Toda lattice, Abundant symmetries for the 1+1 dimensional classical Liouville field theory, A List of 1 + 1 Dimensional Integrable Equations and Their Properties, Soliton structure versus singularity analysis: Third-order completely integrable nonlinear differential equations in \(1+1\)-dimensions, Recursion and Hamiltonian operators for integrable nonabelian difference equations, Normal forms for a class of formulas, Recursion Operator of the Narita–Itoh–Bogoyavlensky Lattice, A symbolic algorithm for computing recursion operators of nonlinear partial differential equations, Recursion operators admitted by non-abelian Burgers equations: some remarks, Lenard scheme for two-dimensional periodic Volterra chain, Rational recursion operators for integrable differential-difference equations, Structural properties of the noncommutative KdV recursion operator

Uses Software

• Maple
• MACSYMA
• LIE0

Cites Work

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• Automatically determining symmetries of partial differential equations
• Symplectic structures, their Bäcklund transformations and hereditary symmetries
• A Method for Finding N-Soliton Solutions of the K.d.V. Equation and K.d.V.-Like Equation
• The Lie Algebra Structure of Nonlinear Evolution Equations Admitting Infinite Dimensional Abelian Symmetry Groups
• The Lie Algebra Structure of Degenerate Hamiltonian and Bi-Hamiltonian Systems
• Mastersymmetries, Higher Order Time-Dependent Symmetries and Conserved Densities of Nonlinear Evolution Equations
• Application of hereditary symmetries to nonlinear evolution equations
• The bi-Hamiltonian structure of some nonlinear fifth- and seventh-order differential equations and recursion formulas for their symmetries and conserved covariants
• On the use of isospectral eigenvalue problems for obtaining hereditary symmetries for Hamiltonian systems
• A new hierarchy of Korteweg–de Vries equations