Journal of Nonlinear Mathematical Physics

Volume 25, Issue 4, July 2018
Letter to Editor

1. On a surface isolated by Gambier

Runliang Lin, Robert Conte
Pages: 509 - 514
We provide a Lax pair for the surfaces of Voss and Guichard, and we show that such particular surfaces considered by Gambier are characterized by a third Painlevé function.
Letter to Editor

2. Solvable nonlinear discrete-time evolutions and Diophantine findings

Francesco Calogero
Pages: 515 - 517
Certain nonlinearly-coupled systems of N discrete-time evolution equations are identified, which can be solved by algebraic operations; and some remarkable Diophantine findings are thereby obtained. These results might be useful to test the accuracy of numerical routines yielding the N roots of polynomials...
Research Article

3. Free-field realizations of the W𝒜n,N-algebra

Yanyan Ge, Kelei Tian, Xiaoming Zhu, Dafeng Zuo
Pages: 518 - 527
In this paper, we will construct free-field realizations of the W𝒜n,N algebra associated to an 𝒜n -valued differential operator 𝒧=In∂N+UN−1∂N−1+UN−2∂N−2+⋯U0, where 𝒜n is a Frobenius algebra with the unit In.
Research Article

4. Composition of Lie Group Elements from Basis Lie Algebra Elements

George W. Bluman, Omar Mrani-Zentar, Deshin Finlay
Pages: 528 - 557
It is shown explicitly how one can obtain elements of Lie groups as compositions of products of other elements based on the commutator properties of associated Lie algebras. Problems of this kind can arise naturally in control theory. Suppose an apparatus has mechanisms for moving in a limited number...
Research Article

5. Singular Hartree equation in fractional perturbed Sobolev spaces

Alessandro Michelangeli, Alessandro Olgiati, Raffaele Scandone
Pages: 558 - 588
We establish the local and global theory for the Cauchy problem of the singular Hartree equation in three dimensions, that is, the modification of the non-linear Schrödinger equation with Hartree non-linearity, where the linear part is now given by the Hamiltonian of point interaction. The latter is...
Research Article

6. Morphisms Cohomology and Deformations of Hom-algebras

Anja Arfa, Nizar Ben Fraj, Abdenacer Makhlouf
Pages: 589 - 603
The purpose of this paper is to define cohomology complexes and study deformation theory of Hom-associative algebra morphisms and Hom-Lie algebra morphisms. We discuss infinitesimal deformations, equivalent deformations and obstructions. Moreover, we provide various examples.
Research Article

7. Lie point symmetries and ODEs passing the Painlevé test

D. Levi, D. Sekera, P. Winternitz
Pages: 604 - 617
The Lie point symmetries of ordinary differential equations (ODEs) that are candidates for having the Painlevé property are explored for ODEs of order n = 2, . . . , 5. Among the 6 ODEs identifying the Painlevé transcendents only PIII, PV and PVI have nontrivial symmetry algebras and that only for very...
Research Article

8. Generating functions for characters and weight multiplicities of irreducible 𝓈𝓁(4)-modules

José Ferńandez Núñez, Wifredo García Fuertes, Askold M. Perelomov
Pages: 618 - 632
Generating functions for the characters of the irreducible representations of simple Lie algebras are rational functions where both the numerator and denominator can be expressed as polynomials in the characters corresponding to the fundamental weights. They encode much information on the representation...
Research Article

9. Riemann-Hilbert approach and N-soliton formula for a higher-order Chen-Lee-Liu equation

Juan Hu, Jian Xu, Guo-Fu Yu
Pages: 633 - 649
We consider a higher-order Chen-Lee-Liu (CLL) equation with third order dispersion and quintic nonlinearity terms. In the framework of the Riemann-Hilbert method, we obtain the compact N-soliton formula expressed by determinants. Based on the determinant solution, some properties for single soliton and...
Review Article

10. Homogeneous Isotropic Turbulence: Geometric and Isometry Properties of the 2-point Velocity Correlation Tensor

Vladimir N. Grebenev, Martin Oberlack
Pages: 650 - 672
The emphasis of this review is both the geometric realization of the 2-point velocity correlation tensor field Bij(x,x′,t) and isometries of the correlation space K3 equipped with a (pseudo-) Riemannian metrics ds2(t) generated by the tensor field. The special form of this tensor field for homogeneous...