Pages: 324 - 340
In this paper we attempt to establish some tauberian theorems in quantum calculus.
This constitutes the beginning of the study of the q-analogue of analytic theory of
numbers which is the aim of a forthcoming paper.
Pages: 388 - 397
In A. Poltorak's concept, the reference frame in General Relativity is a certain manifold
equipped with a connection. The question under consideration here is whether it is
possible to join two events in the space-time by a time-like geodesic if they are joined
by a geodesic of the reference frame...
Pages: 311 - 320
We describe the physical hypothesis in which an approximate model of water waves is
obtained. For an irrotational unidirectional shallow water flow, we derive the Camassa-
Holm equation by a variational approach in the Lagrangian formalism.
Pages: 578 - 588
Some spherical solutions of the ideal magnetohydrodynamic (MHD) equations are
obtained from the method of the weak transversality method (WTM), which is based
on Lie group theory. This analytical method makes use of the symmetry group of the
MHD system in situations where the â€œclassicalâ€ Lie...
Pages: 548 - 569
Deformations of the 3-differential of 3-differential graded algebras are controlled by
the (3, N ) Maurer-Cartan equation. We find explicit formulae for the coefficients
appearing in that equation, introduce new geometric examples of N -differential graded
algebras, and use these results to study...
Pages: 589 - 611
Nonlocal symmetries for exactly integrable three-field evolutionary systems have been com-
puted. Differentiation the nonlocal symmetries with respect to x gives a few hyperbolic
systems for each evolution system. Zero curvature representations for all nonlocal systems
and for some of the hyperbolic...
Pages: 104 - 116
The superposition formulas for solutions of integrable vector evolutionary equations on
a sphere are constructed by means of auto-B ?acklund transformation. The equations
under consideration were obtained earlier by Sokolov and Meshkov in the frame of the
Pages: 48 - 65
We introduce a (2+1)-dimensional extension of the 1-dimensional Toda lattice hierar-
chy. The hierarchy is given by two different formulations. For the first formulation,
we obtain the bilinear identity for the ? -functions and construct explicit solutions ex-
pressed by Wronski determinants. For...
Pages: 205 - 211
We use a method inspired by the Jacobi last multiplier [M.C. Nucci, Jacobi last
multiplier and Lie symmetries: a novel application of an old relationship, J. Nonlinear
Math. Phys. 12, 284-304 (2005)] in order to find Lie symmetries of a Painlev ?e-type
equation without Lie point symmetries.
Pages: 87 - 95
We present a simple approach showing that Gerstner’s flow is dynamically possible: each particle moves on a circle, but the particles never collide and fill out the entire region below the surface wave.
Pages: 1 - 12
The Camassa-Holm (CH) and Hunter-Saxton (HS) equations have an interpretation as geodesic flow equations on the group of diffeomorphisms, preserving the H 1 and H 1 right-invariant metrics correspondingly. There is an analogy to the Euler equations in hydrodynamics, which describe geodesic flow for a...
Pages: 116 - 132
The Burgers equation and the Camassa-Holm equations can both be recast as the
Euler equation for a right-invariant metric on the diffeomorphism group of the circle, the L 2-metric for Burgers and the H 1-metric for Camassa-Holm. Their geometric behaviors are however very different. We present a survey...
Pages: 165 - 178
We construct all partial Noether operators corresponding to a partial agrangian for a system with two degrees of freedom. Then all the first integrals are obtained explicitly by utilizing a Noether-like theorem with the help of the partial Noether operators. We show how the first integrals can be constructed...
Pages: 105 - 111
The nonlinear wave equation with variable long wave velocity and the Gordon-type
equations (in particular, the omega-model equation) display a range of symmetry generators, inter alia, translations, Lorentz rotations and scaling - all of which are related to conservation laws. We do a study of the...
Pages: 192 - 202
The boundary value problems for the two-dimensional, steady, irrotational flow of a frictionless, incompressible fluid past a wedge and a circular cylinder are considered. It is shown that by considering first the invariance of the boundary condition we are able to obtain a transformation group that...
Pages: 112 - 123
We obtain a complete invariant characterization of scalar linear (1+1) parabolic equations under equivalence transformations for all the four canonical forms. Firstly semi-invariants under changes of independent and dependent variables and the construction of the relevant transformations that relate...
Pages: 203 - 210
We present the Lie point symmetries admitted by third order partial differential equations (PDEs) which model the pressure of a visco-elastic liquid with relaxation which filtrates through a porous medium. The symmetries are used to construct reductions of the PDEs to ordinary differential equations...
Pages: 310 - 322
We discuss how the Camassa-Holm hierarchy can be framed within the geometry of the Sato
Grassmannian. We discuss the geometry of an extension of the negative flows of the CH
hierarchy, recover the well-known CH equations, and frame the problem within the theory of
Pages: 176 - 184
We describe the problem of finding a harmonic map between noncompact manifold. Given
some sufficient conditions on the domain, the target and the initial map, we prove the existence
of a harmonic map that deforms the given map.
Pages: 102 - 111
In this work we discuss the complete synchronization of two identical double-well Duffing
oscillators unidirectionally coupled, from the point of view of symbolic dynamics. Working
with Poincaré cross-sections and the return maps associated, the synchronization of the two
oscillators, in terms of...
Pages: 81 - 90
In this paper, the family of BBM equation with strong nonlinear dispersive B(m,n) is considered. We apply the classical Lie method of infinitesimals. The symmetry reductions are
derived from the optimal system of subalgebras and lead to systems of ordinary differential
equations. We obtain for special...
Pages: 396 - 406
We present a geometric analysis of the model of Stirling et al. . In particular we analyze
the curvature of a heart rate time series in response to a step like increment in the exercise
intensity. We present solutions for the point of maximum curvature which can be used as a
marker of physiological...
Pages: 323 - 333
We apply the discrete multiscale expansion to the Lax pair and to the first few symmetries
of the lattice potential Korteweg-de Vries equation. From these calculations we show that,
like the lowest order secularity conditions give a nonlinear SchrÂ¨odinger equation, the Lax pair
gives at the same...
Pages: 333 - 347
A method is proposed in this paper to construct a new extended q-deformed KP (q-KP) hiearchy and its Lax representation. This new extended q-KP hierarchy contains two types of q-deformed KP equation with self-consistent sources, and its two kinds of reductions give the q-deformed Gelfand-Dickey hierarchy...
Pages: 365 - 382
In this paper we compute first integrals of nonlinear ordinary differential equations using the extended Prelle-Singer method, as formulated by Chandrasekar et al in J. Math. Phys. 47 (2), 023508, (2006). We find a new first integral for the Painlev´e-Gambier XXII equation. We also derive the first integrals...
Pages: 69 - 82
The proposed relational fuzzy clustering method, called FRFP ( fuzzy relational fixed point), is based on determining a
fixed point of a function of the desired membership matrix. The ethod is compared to other relational clustering
methods. Simulations show the method to be very effective and less...
Pages: 323 - 351
We prove that, for the irreducible complex crystallographic Coxeter group W, the
following conditions are equivalent: a) W is generated by reflections;
b) the analytic variety X/W is isomorphic to a weighted projective space.
The result is of interest, for example, in application to topological conformal...
Pages: 441 - 466
The Korteweg de Vries (KdV) equation is well known as an approximation model
for small amplitude and long waves in different physical contexts, but wave breaking phenomena related to short wavelengths are not captured in. In this work we consider a class of nonlocal dispersive wave equations which...
Pages: 95 - 106
This paper is devoted to an extension of Burchnall-Chaundy theory on the inteplay between algebraic geometry and commuting differential operators to the case of
Pages: 238 - 245
A coupled Toda equation and its related equation are derived from 3-coupled bilinear
equations. The corresponding Bäcklund transformation and nonlinear superposition
formula are presented for the 3-coupled bilinear equations. As an application of the
results, solition solutions are derived. Besides,...
Pages: 62 - 71
The derivative nonlinear Schrödinger equation is shown to be locally well-posed in
a class of functions analytic on a strip around the real axis. The main feature of the
result is that the width of the strip does not shrink in time. To overcome the derivative
loss, Kato-type smoothing results and...
Pages: 93 - 106
It is proven that the essential spectrum of any self-adjoint operator associated with
the matrix differential expression
Pages: 141 - 147
We observe a correspondence between the zero modes of superconformal algebras
S (2, 1) and W(4) () and the Lie superalgebras formed by classical operators apearing in the Kähler and hyper-Kähler geometry.
Pages: 136 - 140
) be the space of tensor densities on Sn
of degree . We consider this space
as an induced module of the nonunitary spherical series of the group SO0(n+1, 1) and
classify (so(n+1, 1), SO(n+1))-simple and unitary submodules of F(Sn
) as a function
Pages: 229 - 242
We present a theory of compatible differential constraints of a hydrodynamic hierarchy
of infinite-dimensional systems. It provides a convenient point of view for studying
and formulating integrability properties and it reveals some hidden structures of the
theory of integrable systems. Illustrative...
Pages: 16 - 50
In this letter we present the set of invariant difference equations and meshes which
preserve the Lie group symmetries of the equation ut = (K(u)ux)x +Q(u). All special
cases of K(u) and Q(u) that extend the symmetry group admitted by the differential
equation are considered. This paper completes...
Pages: 65 - 77
In this work, we explain in what sense the generic level set of the constants of motion
for the periodic nonlinear Schrödinger equation is an infinite dimensional torus on
which each generalized nonlinear Schrödinger flow is reduced to straight line almost
periodic motion, and describe how neighboring...
Pages: 426 - 445
We establish the incompressible NavierStokes limit for the discrete velocity model of
the Boltzmann equation in any dimension of the physical space, for densities which rmain in a suitable small neighborhood of the global Maxwellian. Appropriately scaled
families solutions of discrete Boltzmann equation...
Pages: 446 - 454
A one phase Stefan problem in nonlinear conduction is considered. The problem is
shown to admit a unique solution for small times. An exact solution is obtained which
is a travelling front moving with constant speed.
Pages: 1 - 9
The reduction of nonlinear ordinary differential equations by a combination of first
integrals and Lie group symmetries is investigated. The retention, loss or even gain
in symmetries in the integration of a nonlinear ordinary differential equation to a first
integral are studied for several examples....
Pages: 347 - 356
We compute the Poisson cohomology of the one-parameter family of SU(2)-covariant
Poisson structures on the homogeneous space S2
= SU(2)/U(1), where SU(2)
is endowed with its standard PoissonLie group structure, thus extending the result
of Ginzburg  on the BruhatPoisson structure which...
Pages: 325 - 346
We consider a wide class of model equations, able to describe wave propagation in
dispersive nonlinear media. The Korteweg-de Vries (KdV) equation is derived in this
general frame under some conditions, the physical meanings of which are clarified.
It is obtained as usual at leading order in some...
Pages: 282 - 310
Starting from the second Painlevé equation, we obtain Painlevé type equations of
higher order by using the singular point analysis.
Pages: 126 - 143
A new type of perturbative expansion is built in order to give a rigorous derivation
and to clarify the range of validity of some commonly used model equations. This
model describes the evolution of the modulation of two short and localized pulses,
fundamental and second harmonic, propagating together...
Pages: 152 - 163
It is known that many integrable systems can be reduced from self-dual Yang-Mills
equations. The formal solution space to the self-dual Yang-Mills equations is given by
the so called ADHM construction, in which the solution space are graded by vector
spaces with dimensionality concerning topological...
Pages: 127 - 139
Hirota's bilinear technique is applied to some integrable lattice systems related to
the Bäcklund transformations of the 2DToda, Lotka-Volterra and relativistic LotkVolterra lattice systems, which include the modified Lotka-Volterra lattice system,
the modified relativistic Lotka-Volterra lattice system,...
Pages: 99 - 105
We investigate linear stability of solitary waves of a Hamiltonian system. Unlike
weakly nonlinear water wave models, the physical system considered here is nonlinearly
dispersive, and contains nonlinearity in its highest derivative term. This results in
more detailed asymptotic analysis of the eigenvalue...
Pages: 29 - 46
There is a wide class of integrable Hamiltonian systems on finite-dimensional coadjoint
orbits of the loop algebra ~gl(r) which are represented by r × r Lax equations with a
rational spectral parameter. A reduced complex phase space is foliated with open
subsets of Jacobians of regularized spectral...
Pages: 1 - 10
Qualitative approach to homogeneous anisotropic Bianchi class A models in terms
of dynamical systems reveals a hierarchy of invariant manifolds. By calculating the
Kovalevski Exponents according to Adler - van Moerbecke method we discuss how
algebraic integrability property is distributed in this...
Pages: 26 - 41
We give a hierarchy of many-parameter families of maps of the interval [0, 1] with an
invariant measure and using the measure, we calculate KolmogorovSinai entropy of
these maps analytically. In contrary to the usual one-dimensional maps these maps
do not possess period doubling or period-n-tupling...