173 research outputs found
A 2-Component Generalization of the Camassa-Holm Equation and Its Solutions
An explicit reciprocal transformation between a 2-component generalization of
the Camassa-Holm equation, called the 2-CH system, and the first negative flow
of the AKNS hierarchy is established, this transformation enables one to obtain
solutions of the 2-CH system from those of the first negative flow of the AKNS
hierarchy. Interesting examples of peakon and multi-kink solutions of the 2-CH
system are presented.Comment: 15 pages, 16 figures, some typos correcte
Tension and stiffness of the hard sphere crystal-fluid interface
A combination of fundamental measure density functional theory and Monte
Carlo computer simulation is used to determine the orientation-resolved
interfacial tension and stiffness for the equilibrium hard-sphere crystal-fluid
interface. Microscopic density functional theory is in quantitative agreement
with simulations and predicts a tension of 0.66 kT/\sigma^2 with a small
anisotropy of about 0.025 kT and stiffnesses with e.g. 0.53 kT/\sigma^2 for the
(001) orientation and 1.03 kT/\sigma^2 for the (111) orientation. Here kT is
denoting the thermal energy and \sigma the hard sphere diameter. We compare our
results with existing experimental findings
On Soliton-type Solutions of Equations Associated with N-component Systems
The algebraic geometric approach to -component systems of nonlinear
integrable PDE's is used to obtain and analyze explicit solutions of the
coupled KdV and Dym equations. Detailed analysis of soliton fission, kink to
anti-kink transitions and multi-peaked soliton solutions is carried out.
Transformations are used to connect these solutions to several other equations
that model physical phenomena in fluid dynamics and nonlinear optics.Comment: 43 pages, 16 figure
Staeckel systems generating coupled KdV hierarchies and their finite-gap and rational solutions
We show how to generate coupled KdV hierarchies from Staeckel separable
systems of Benenti type. We further show that solutions of these Staeckel
systems generate a large class of finite-gap and rational solutions of cKdV
hierarchies. Most of these solutions are new.Comment: 15 page
Generalized r-matrix structure and algebro-geometric solution for integrable systems
The purpose of this paper is to construct a generalized r-matrix structure of
finite dimensional systems and an approach to obtain the algebro-geometric
solutions of integrable nonlinear evolution equations (NLEEs). Our starting
point is a generalized Lax matrix instead of usual Lax pair. The generalized
r-matrix structure and Hamiltonian functions are presented on the basis of
fundamental Poisson bracket. It can be clearly seen that various nonlinear
constrained (c-) and restricted (r-) systems, such as the c-AKNS, c-MKdV,
c-Toda, r-Toda, c-Levi, etc, are derived from the reduction of this structure.
All these nonlinear systems have {\it r}-matrices, and are completely
integrable in Liouville's sense. Furthermore, our generalized structure is
developed to become an approach to obtain the algebro-geometric solutions of
integrable NLEEs. Finally, the two typical examples are considered to
illustrate this approach: the infinite or periodic Toda lattice equation and
the AKNS equation with the condition of decay at infinity or periodic boundary.Comment: 41 pages, 0 figure
シンサイ ニツイテ タイワスル コドモ ノ テツガク ノ カノウセイ
International audienc
Reduction of bihamiltonian systems and separation of variables: an example from the Boussinesq hierarchy
We discuss the Boussinesq system with stationary, within a general
framework for the analysis of stationary flows of n-Gel'fand-Dickey
hierarchies. We show how a careful use of its bihamiltonian structure can be
used to provide a set of separation coordinates for the corresponding
Hamilton--Jacobi equations.Comment: 20 pages, LaTeX2e, report to NEEDS in Leeds (1998), to be published
in Theor. Math. Phy
Classical Poisson structures and r-matrices from constrained flows
We construct the classical Poisson structure and -matrix for some finite
dimensional integrable Hamiltonian systems obtained by constraining the flows
of soliton equations in a certain way. This approach allows one to produce new
kinds of classical, dynamical Yang-Baxter structures. To illustrate the method
we present the -matrices associated with the constrained flows of the
Kaup-Newell, KdV, AKNS, WKI and TG hierarchies, all generated by a
2-dimensional eigenvalue problem. Some of the obtained -matrices depend only
on the spectral parameters, but others depend also on the dynamical variables.
For consistency they have to obey a classical Yang-Baxter-type equation,
possibly with dynamical extra terms.Comment: 16 pages in LaTe
On Separation of Variables for Integrable Equations of Soliton Type
We propose a general scheme for separation of variables in the integrable
Hamiltonian systems on orbits of the loop algebra
. In
particular, we illustrate the scheme by application to modified Korteweg--de
Vries (MKdV), sin(sinh)-Gordon, nonlinear Schr\"odinger, and Heisenberg
magnetic equations.Comment: 22 page
Hodograph solutions of the dispersionless coupled KdV hierarchies, critical points and the Euler-Poisson-Darboux equation
It is shown that the hodograph solutions of the dispersionless coupled KdV
(dcKdV) hierarchies describe critical and degenerate critical points of a
scalar function which obeys the Euler-Poisson-Darboux equation. Singular
sectors of each dcKdV hierarchy are found to be described by solutions of
higher genus dcKdV hierarchies. Concrete solutions exhibiting shock type
singularities are presented.Comment: 19 page
- …