| 1. |
- Bennewitz, Christer
(author)
-
On the spectral problem associated with the Camassa-Holm equation
- 2004
-
In: Journal of Nonlinear Mathematical Physics. - : Springer Science and Business Media LLC. - 1402-9251 .- 1776-0852. ; 11:4, s. 422-434
-
Journal article (peer-reviewed)abstract
- We give a basic uniqueness theorem in the inverse spectral theory for a Sturm-Liouville equation with a weight which is not of one sign. It is shown that the theorem may be applied to the spectral problem associated with the Camassa-Holm integrable system which models shallow water waves.
|
|
| 2. |
- Bobylev, Alexander, 1947-, et al.
(author)
-
Group analysis of the generalized Burnett equations
- 2020
-
In: Journal of Nonlinear Mathematical Physics. - : Taylor & Francis. - 1402-9251 .- 1776-0852. ; 27:3, s. 494-494
-
Journal article (peer-reviewed)abstract
- In this paper group properties of the so-called Generalized Burnett equations are studied. In contrast to the clas-sical Burnett equations these equations are well-posed and therefore can be used in applications. We considerthe one-dimensional version of the generalized Burnett equations for Maxwell molecules in both Eulerian andLagrangian coordinates and perform the complete group analysis of these equations. In particular, this includesfinding and analyzing admitted Lie groups. Our classifications of the Lie symmetries of the Navier-Stokes equa-tions of compressible gas and generalized Burnett equations provide a basis for finding invariant solutions ofthese equations. We also consider representations of all invariant solutions. Some particular classes of invariantsolutions are studied in more detail by both analytical and numerical methods
|
|
| 3. |
|
|
| 4. |
- Byström, Johan
(author)
-
Correctors for some nonlinear monotone operators
- 2001
-
In: Journal of Nonlinear Mathematical Physics. - : Springer Science and Business Media LLC. - 1402-9251 .- 1776-0852. ; 8:1, s. 8-30
-
Journal article (peer-reviewed)abstract
- In this paper we study homogenization of quasi-linear partial differential equations of the form -div (a (x, x/εh,Duh)) = fh on Ω with Dirichlet boundary conditions. Here the sequence (εh) tends to 0 as h→∞ and the map a (x, y, ξ) is periodic in y, monotone in ξ and satisfies suitable continuity conditions.W e prove that uh → u weakly in W1,p 0 (Ω) as h → ∞, where u is the solution of a homogenized problem of the form -div (b (x,Du)) = f on Ω. We also derive an explicit expression for the homogenized operator b and prove some corrector results, i.e. we find (Ph) such that Duh -Ph (Du) → 0 in Lp (Ω,Rn). () 0 in (Ω).
|
|
| 5. |
- Carillo, Sandra, et al.
(author)
-
On the recursion operator for the noncommutative Burgers hierarchy
- 2012
-
In: Journal of Nonlinear Mathematical Physics. - 1402-9251 .- 1776-0852. ; 19:1, s. Art. no. 1250003-
-
Journal article (peer-reviewed)abstract
- The noncommutative Burgers recursion operator is constructed via the ColeHopf transformation, and its structural properties are studied. In particular, a direct proof of its hereditary property is given. © S. Carillo and C. Schiebold.
|
|
| 6. |
- Chanfreau, Philippe, et al.
(author)
-
Viewing the efficiency of chaos control
- 1999
-
In: Journal of Nonlinear Mathematical Physics. - : Springer Science and Business Media LLC. - 1402-9251 .- 1776-0852. ; 6:3, s. 314-331
-
Journal article (peer-reviewed)abstract
- This paper aims to cast some new light on controlling chaos using the OGY- and the Zero-Spectral-Radius methods. In deriving those methods we use a generalized procedure differing from the usual ones. This procedure allows us to conveniently treat maps to be controlled bringing the orbit to both various saddles and to sources with both real and complex eigenvalues. We demonstrate the procedure and the subsequent control on a variety of maps. We evaluate the control by examining the basins of attraction of the relevant controlled systems graphically and in some cases analytically
|
|
| 7. |
- Chapovalov, Danil, et al.
(author)
-
THE CLASSIFICATION OF ALMOST AFFINE (HYPERBOLIC) LIE SUPERALGEBRAS
- 2010
-
In: Journal of Nonlinear Mathematical Physics. - 1402-9251 .- 1776-0852. ; 17, s. 103-161
-
Journal article (peer-reviewed)abstract
- We say that an indecomposable Cartan matrix A with entries in the ground field is almost affine if the Lie (super) algebra determined by it is not finite dimensional or affine (Kac-Moody) but the Lie sub(super) algebra determined by any submatrix of A, obtained by striking out any row and any column intersecting on the main diagonal, is the sum of finite dimensional or affine Lie (super) algebras. A Lie (super) algebra with Cartan matrix is said to be almost affine if it is not finite dimensional or affine (Kac-Moody), and all of its Cartan matrices are almost affine. We list all almost affine Lie superalgebras over complex numbers with indecomposable Cartan matrix correcting two earlier claims of classification.
|
|
| 8. |
- Chapovalov, Maxim, et al.
(author)
-
THE POINCARE SERIES OF THE HYPERBOLIC COXETER GROUPS WITH FINITE VOLUME OF FUNDAMENTAL DOMAINS
- 2010
-
In: Journal of Nonlinear Mathematical Physics. - 1402-9251 .- 1776-0852. ; 17, s. 169-215
-
Journal article (peer-reviewed)abstract
- The discrete group generated by reflections of the sphere, or the Euclidean space, or hyperbolic space are said to be Coxeter groups of, respectively, spherical, or Euclidean, or hyperbolic type. The hyperbolic Coxeter groups are said to be (quasi-) Lanner if the tiles covering the space are of finite volume and all (resp. some of them) are compact. For any Coxeter group stratified by the length of its elements, the Poincare series is the generating function of the cardinalities of sets of elements of equal length. Around 1966, Solomon established that, for ANY Coxeter group, its Poincare series is a rational function with zeros somewhere on the unit circle centered at the origin, and gave an implicit (recurrence) formula. For the spherical and Euclidean Coxeter groups, the explicit expression of the Poincare series is well-known. The explicit answer was known for any 3-generated Coxeter group, and (with mistakes) for the Lanner groups. Here we give a lucid description of the numerator of the Poincare series of any Coxeter group, the explicit expression of the Poincare series for each Lanner and quasi-Lanner group, and review the scene. We give an interpretation of some coefficients of the denominator of the growth function. The non-real poles behave as in Enestrom's theorem (lie in a narrow annulus) though the coefficients of the denominators do not satisfy theorem's requirements.
|
|
| 9. |
- Cohen, David, et al.
(author)
-
A multi-symplectic numerical integrator for the two-component Camassa Holm equation
- 2014
-
In: Journal of Nonlinear Mathematical Physics. - : Taylor & Francis. - 1402-9251 .- 1776-0852. ; 21:3, s. 442-453
-
Journal article (peer-reviewed)abstract
- A new multi-symplectic formulation of the two-component Camassa-Holm equation (2CH) is presented, and the associated local conservation laws are shown to correspond to certain well-known Hamiltonian functionals. A multi-symplectic discretisation based on this new formulation is exemplified by means of the Euler box scheme. Furthermore, this scheme preserves exactly two discrete versions of the Casimir functions of 2CH. Numerical experiments show that the proposed numerical scheme has good conservation properties.
|
|
| 10. |
- Constantin, Adrian
(author)
-
A Hamiltonian formulation for free surface water waves with non-vanishing vorticity
- 2005
-
In: Journal of Nonlinear Mathematical Physics. - : Springer Science and Business Media LLC. - 1402-9251 .- 1776-0852. ; 12:Suppl. 1, s. 202-211
-
Journal article (peer-reviewed)abstract
- We describe the derivation of a formalism in the context of the governing equations for two-dimensional water waves propagating over a flat bed in a flow with non-vanishing vorticity. This consists in providing a Hamiltonian structure in terms of two variables which are scalar functions.
|
|
