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The Algebro-Geometric Initial Value Problem for the Ruijsenaars-Toda Hierarchy and Quasi-Periodic Solutions
Ruijsenaars-Toda hierarchy complex-valued algebro-geometric solutions hyperelliptic curve Dubrovin-type equation Baker-Akhiezer vector
2012/4/27
We provide a detailed treatment of Ruijsenaars-Toda (RT) hierarchy with special emphasis on its the theta function representation of all algebro-geometric solutions. The basic tools involve hyperellip...
Dunajski-Tod equation and reductions of the generalized dispersionless 2DTL hierarchy
Dunajski-Tod equation reductions of the generalized dispersionless 2DTL hierarchy Exactly Solvable and Integrable Systems
2012/4/26
We transfer the scheme for constructing differential reductions recently developed for the Manakov-Santini hierarchy to the case of the two-component generalization of dispersionless 2DTL hierarchy. W...
The global solutions of algebro-geometric type for Degasperis-Procesi hierarchy
The global solutions of algebro-geometric type Degasperis-Procesi hierarchy Exactly Solvable and Integrable Systems
2012/4/26
Though completely integrable Camassa-Holm (CH) equation and Degasperis-Procesi (DP) equation are cast in the same peakon family, they possess the second- and third-order Lax operators, respectively. F...
Hierarchy of graph matchbox manifolds
matchbox manifold laminations ends of leaves growth of leaves theory of levels GromovHausdorff metric
2011/9/21
Abstract: We study a class of graph foliated spaces, or graph matchbox manifold, initially constructed by Kenyon and Ghys. For graph foliated spaces we introduce a quantifier of dynamical complexity w...
The hierarchy of omega1-Borel sets
Borel hierarchies Martin’s Axiom Q-set Cohen real model Steel forcing
2011/9/20
Abstract: The family omega1-Borel sets is the smallest family of subsets of the real line which contains the family of open sets and is closed under complementation and omega1 unions. We show:
Theor...
Pole-free solutions of the first Painlevé hierarchy and non-generic critical behavior for the KdV equation
the first Painlevé hierarchy non-generic critical behavior the KdV equation
2011/8/23
Abstract: We establish the existence of real pole-free solutions to all even members of the Painlev\'e I hierarchy. We also obtain asymptotics for those solutions and describe their relevance in the d...
Hierarchy of integrable Hamiltonians describing of nonlinear n-wave interaction
nonlinear n-wave Hamiltonians Hierarchy
2011/7/7
In the paper we construct an hierarchy of integrable Hamiltonian systems which describe the variation of n-wave envelopes in nonlinear dielectric medium. The exact solutions for some special Hamiltoni...
A hierarchy of length scales for solutions of the three-dimensional Navier-Stokes equations
hierarchy of length scales for solutions three-dimensional Navier-Stokes equations
2010/12/28
Moments of the vorticity are used to define and estimate a hierarchy of time-averaged inverse length scales λ−1 m for the three-dimensional Navier-Stokes equations on a periodic
box [0, L]3.
The AKNS Hierarchy Integrability Analysis Revisited: The Vertex Operator Approach and its Lie-Algebraic Structure
the AKNS hierarchy Lax type integrability Lie-algebraic approach
2011/3/2
A regular approach to studying the Lax type integrability of the AKNS hierarchy of nonlinear Lax type integrable dynamical systems in the vertex operator representation is devised.
The AKNS Hierarchy Integrability Analysis Revisited: The Vertex Operator Approach and its Lie-Algebraic Structure
the AKNS hierarchy Lax type integrability Lie-algebraic approach vertex operators
2010/12/28
A regular approach to studying the Lax type integrability of the AKNS hierarchy of nonlinear Lax type integrable dynamical systems in the vertex operator representation is devised.
Wrinkling hierarchy in constrained thin sheets from suspended graphene to curtains
constrained thin sheets suspended graphene curtains
2010/12/28
The drive towards miniaturization in technology is demanding for increasingly thinner components,raising new mechanical challenges [1]. Thin lms are however unstable to boundary or substrate-induced ...
The $(N,M)$-bigraded Toda hierarchy is an extension of the original Toda lattice hierarchy. The pair of numbers $(N,M)$ represents the band structure of the Lax matrix which has $N$ upper and $M$ lowe...
A Hierarchy of Local Symplectic Filling Obstructions for Contact 3-Manifolds
Local Symplectic Filling Obstructions Contact 3-Manifolds
2010/12/6
We generalize the familiar notions of overtwistedness and Giroux torsion in 3-dimensional contact manifolds, defining an infinite hierarchy of local filling obstructions called planar torsion, whose i...
Symmetries for the Ablowitz-Ladik hierarchy: II. Integrable discrete nonlinear Schrödinger equation and discrete AKNS hierarchy
Ablowitz-Ladik hierarchy nonlinear Schrö dinger equation discrete AKNS hierarchy
2010/4/21
In the paper we continue to consider symmetries related to the Ablowitz-Ladik hierarchy. We derive symmetries for the integrable discrete nonlinear Schr\"odinger hierarchy and discrete AKNS hierarchy....
Virasoro and W-constraints for the $q$-KP hierarchy
W-constraints $q$-KP hierarchy Adler-Shiota-van Moerbeke
2010/4/6
Based on the Adler-Shiota-van Moerbeke (ASvM) formula, the Virasoro constraints and W-constraints for the p-reduced q-deformed Kadomtsev-Petviashvili (q-KP) hierarchy are established.