KP trigonometric solitons and an adelic flag manifold.
L2 -characteristic classes of Maslov–Trofimov of hamiltonian systems on the Lie algebra of the upper-triangular matrices
We generalize the construction of Maslov-Trofimov characteristic classes to the case of some G-manifolds and use it to study certain hamiltonian systems.
Lagrangian approach to dispersionless KdV hierarchy.
Lax equation representation of certain completely integrable systems
Lax integrable supersymmetric hierarchies on extended phase spaces.
Limit matrices for the Toda flow and periodic flags for loop groups.
Linearising two-dimensional integrable systems and the construction of action-angle variables.
Liouville integrability of geometric variational problems.
Local analyticity in the time and space variables and the smoothing effect for the fifth-order KdV-type equation.
Localized induction equation for stretched vortex filament.
Long time asymptotics of the Camassa–Holm equation on the half-line
We study the long-time behavior of solutions of the initial-boundary value (IBV) problem for the Camassa–Holm (CH) equation on the half-line . The paper continues our study of IBV problems for the CH equation, the key tool of which is the formulation and analysis of associated Riemann–Hilbert factorization problems. We specify the regions in the quarter space-time plane , having qualitatively different asymptotic pictures, and give the main terms of the asymptotics in terms of spectral data...
Minimal tori in S4.
Models for quadratic algebras associated with second order superintegrable systems in 2D.
Modulation of the Camassa-Holm equation and reciprocal transformations
We derive the modulation equations (Whitham equations) for the Camassa-Holm (CH) equation. We show that the modulation equations are hyperbolic and admit a bi-Hamiltonian structure. Furthermore they are connected by a reciprocal transformation to the modulation equations of the first negative flow of the Korteweg de Vries (KdV) equation. The reciprocal transformation is generated by the Casimir of the second Poisson bracket of the KdV averaged flow. We show that the geometry...
Moving frames, Geometric Poisson brackets and the KdV-Schwarzian evolution of pure spinors
In this paper we describe a non-local moving frame along a curve of pure spinors in , and its associated basis of differential invariants. We show that the space of differential invariants of Schwarzian-type define a Poisson submanifold of the spinor Geometric Poisson brackets. The resulting restriction is given by a decoupled system of KdV Poisson structures. We define a generalization of the Schwarzian-KdV evolution for pure spinor curves and we prove that it induces a decoupled system of KdV...
Multicomponent Burgers and KP hierarchies, and solutions from a matrix linear system.
Multi-symplectic Fourier pseudospectral method for the nonlinear Schrödinger equation.
-wave equations with orthogonal algebras: and reductions and soliton solutions.
New exact solutions for the -dimensional Broer-Kaup-Kupershmidt equations.
Nilpotent and recursive flows.