Scaling invariant Lax pairs of nonlinear evolution equations

DOI10.1080/00036811.2011.629611zbMath1247.37046arXiv1110.0586OpenAlexW2043079323WikidataQ58134745 ScholiaQ58134745MaRDI QIDQ3225849

Jennifer Larue, Ünal Göktaş, M. S. Hickman, Willy Hereman

Publication date: 22 March 2012

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.0586

zbMATH Keywords

complete integrabilityLax pairLax operatorscaling symmetryfifth-order KdV-type equations

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Soliton equations (35Q51) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Nonlinear evolution equations (47J35)

Related Items (4)

Lie symmetry analysis, Lie-Bäcklund symmetries, explicit solutions, and conservation laws of Drinfeld-Sokolov-Wilson system ⋮ Reductions of PDEs to second order ODEs and symbolic computation ⋮ Two new reductions methods for polynomial differential equations and applications to nonlinear pdes ⋮ A new method to obtain either first- or second-order reductions for parametric polynomial ODEs

Uses Software

• Maple
• Mathematica
• LaxPairPartialDifferenceEquations

Cites Work

• Solitons and infinite dimensional Lie algebras
• Lie algebras and equations of Korteweg-de Vries type
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• A Bäcklund Transformation for a Higher Order Korteweg-De Vries Equation
• An Extension of Nonlinear Evolution Equations of the K-dV (mK-dV) Type to Higher Orders
• Algorithmic method for deriving Lax pairs from the invariant Painlevé analysis of nonlinear partial differential equations
• The Painlevé property for partial differential equations
• On the Inverse Scattering Problem for Cubic Eigenvalue Problems of the Class ψ_xxx + 6Qψ_x + 6R_ψ = λψ
• Factorization of operators I. Miura transformations
• Prolongation structures of nonlinear evolution equations
• Prolongation structures of nonlinear evolution equations. II
• A new hierarchy of Korteweg–de Vries equations
• The prolongation structure of a higher order Korteweg-de Vries equation
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• On construction of recursion operators from Lax representation
• Pseudo-differential Operators and Generalized Lax Equations in Symbolic Computation
• Integrals of nonlinear equations of evolution and solitary waves

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