On `regular' and `anomalous' solitons of fifth-order equations and an iteration method

DOI10.1016/S0034-4877(01)80026-4zbMath0976.35068MaRDI QIDQ5942387

Allen Parker

Publication date: 29 August 2001

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Hirota's bilinear transformKaup-Kupershmidt equationSawada-Kotera equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Soliton equations (35Q51) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40)

Cites Work

• Symbolic methods to construct exact solutions of nonlinear partial differential equations
• Solitons and infinite dimensional Lie algebras
• Bilinear transformation method
• On soliton solutions of the Kaup-Kupershmidt equation. I: Direct bilinearisation and solitary wave
• On soliton solutions of the Kaup-Kupershmidt equation. II: `Anomalous' \(N\)-soliton solutions
• A Method for Finding N-Soliton Solutions of the K.d.V. Equation and K.d.V.-Like Equation
• A Bäcklund Transformation for a Higher Order Korteweg-De Vries Equation
• On classes of integrable systems and the Painlevé property
• KP Hierarchies of Orthogonal and Symplectic Type–Transformation Groups for Soliton Equations VI–
• On the Inverse Scattering Problem for Cubic Eigenvalue Problems of the Class ψ_xxx + 6Qψ_x + 6R_ψ = λψ
• Existence and Nonexistence of Solitary Wave Solutions to Higher-Order Model Evolution Equations
• The inverse scattering transform: Semi-infinite interval
• A new hierarchy of Korteweg–de Vries equations
• Third order spectral problems: reductions and Darboux transformations
• On reciprocal properties of the Caudrey-Dodd-Gibbon and Kaup-Kupershmidt hierarchies
• Bäcklund transformation of partial differential equations from the Painlevé–Gambier classification. I. Kaup–Kupershmidt equation
• Theory of a Solid State Plasma Waveguide in a Transverse Magnetic Field