Higher-Order Nonlinear Dynamical Systems and Invariant Lagrangians on a Lie Group: The Case of Nonlocal Hunter–Saxton Type Peakons

DOI10.1007/S12346-024-01018-8MaRDI QIDQ6498608

Waranont Anukool, Ahmad Rami El-Nabulsi

Publication date: 7 May 2024

Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)

Lie algebras of vector fields and related (super) algebras (17B66) Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems (70S05) Euler-Poisson-Darboux equations (35Q05)

Cites Work

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A nonlinear generalization of the Camassa-Holm equation with peakon solutions
\(G\)-strands and peakon collisions on \(\text{Diff}(\mathbb R)\)
Higher order Lagrange-Poincaré and Hamilton-Poincaré reductions
Chaotic and fractal patterns for interacting nonlinear waves
Well-posedness and blow-up phenomena for a higher order shallow water equation
Extending Newton's law from nonlocal-in-time kinetic energy
Invariant higher-order variational problems
\(G\)-strands
Invariant higher-order variational problems. II
Euler-Lagrange equation from nonlocal-in-time kinetic energy of nonconservative system
General \(N\)-solitons and their dynamics in several nonlocal nonlinear Schrödinger equations
The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
Nonlocal models for nonlinear, dispersive waves
Lagrangian submanifolds and the Euler-Lagrange equations in higher-order mechanics
Generalized Hunter-Saxton equation and the geometry of the group of circle diffeomorphisms
Poisson brackets and clebsch representations for magnetohydrodynamics, multifluid plasmas, and elasticity
The geometric structure of complex fluids
Well-posedness of modified Camassa-Holm equations
On the Hunter-Saxton system
The Euler-Poincaré equations and semidirect products with applications to continuum theories
Wave breaking for nonlinear nonlocal shallow water equations
On a completely integrable nonlinear hyperbolic variational equation
Algebro-geometric solutions of the Camassa-Holm hierarchy
Hamiltonian structure of peakons as weak solutions for the modified Camassa-Holm equation
Breather, lump and \(X\) soliton solutions to nonlocal KP equation
Integrable \(U(1)\)-invariant peakon equations from the NLS hierarchy
Complex backward-forward derivative operator in non-local-in-time Lagrangians mechanics
Lax integrability and the peakon problem for the modified Camassa-Holm equation
Euler equations on homogeneous spaces and Virasoro orbits
Stability in integrable nonlocal nonlinear equations
Convergence rate of the vanishing viscosity limit for the Hunter-Saxton equation in the half space
Solitons, breathers and rogue waves in the coupled nonlocal reverse-time nonlinear Schrödinger equations
Symmetry breaking soliton, breather, and lump solutions of a nonlocal Kadomtsev-Petviashvili system
Integrability structures of the generalized Hunter-Saxton equation
On nonlocal fractal laminar steady and unsteady flows
Accelerating dynamical peakons and their behaviour
The Hunter-Saxton equation describes the geodesic flow on a sphere
Geodesic flow and two (super) component analog of the Camassa-Holm equation
Sur la géométrie différentielle des groupes de Lie de dimension infinite et ses applications à l'hydrodynamique des fluides parfaits
Asymptotic Blowup Profiles for Modified Camassa–Holm Equations
Euler-Poincaré Dynamics of Perfect Complex Fluids
On a class of nonlocal wave equations from applications
A family of wave-breaking equations generalizing the Camassa-Holm and Novikov equations
The Hunter–Saxton Equation: A Geometric Approach
Dynamics of Director Fields
A shallow water equation on the circle
An integrable shallow water equation with peaked solitons
Integrable Nonlocal Nonlinear Equations
G -Strands on symmetric spaces
Integrable nonlocal nonlinear Schrödinger equations associated with 𝑠𝑜(3,ℝ)
A general family of multi-peakon equations and their properties
Nonlinear wave equations from a non-local complex backward–forward derivative operator
The r-Hunter–Saxton equation, smooth and singular solutions and their approximation
Periodic and hyperbolic soliton solutions of a number of nonlocal nonlinear equations
Colliding peakons and the formation of shocks in the Degasperis–Procesi equation
The Generalized Hunter–Saxton System
Peakon-antipeakon interactions in the Degasperis-Procesi equation

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