Journal of Nonlinear Mathematical Physics

Volume 28, Issue 2, June 2021
Research Article

1. Exact Solutions of a Nonlinear Diffusion Equation with Absorption and Production

Robert Conte
Pages: 171 - 181
We provide closed form solutions for an equation which describes the transport of turbulent kinetic energy in the framework of a turbulence model with a single equation.
Research Article

2. Symmetries of Kolmogorov Backward Equation

Roman Kozlov
Pages: 182 - 193
The note provides the relation between symmetries and first integrals of Itô stochastic differential equations and symmetries of the associated Kolmogorov Backward Equation (KBE). Relation between the symmetries of the KBE and the symmetries of the Kolmogorov forward equation is also given.
Research Article

3. Compatible Poisson Structures and bi-Hamiltonian Systems Related to Low-dimensional Lie Algebras

Gh. Haghighatdoost, S. Abdolhadi-Zangakani, J. Abedi-Fardad
Pages: 194 - 204
In this work, we give a method to construct compatible Poisson structures on Lie groups by means of structure constants of their Lie algebras and some vector field. In this way we calculate some compatible Poisson structures on low-dimensional Lie groups. Then, using a theorem by Magri and Morosi, we...
Research Article

4. Orbits and Lagrangian Symmetries on the Phase Space

Javier Pérez Álvare
Pages: 205 - 208
In this article, given a regular Lagrangian system L on the phase space TM of the configuration manifold M and a 1-parameter group G of transformations of M whose lifting to TM preserve the canonical symplectic dynamics associated to L, we determine conditions so that its infinitesimal generator produces...
Research Article

5. On Ramsey Dynamical Model and Closed-Form Solutions

Gülden Gün Polat, Teoman Özer
Pages: 209 - 218
This study focuses on the analysis of Ramsey dynamical model with current Hamiltonian defining an optimal control problem in a neoclassical growth model by utilizing Lie group theory. Lie point symmetries of coupled nonlinear first-order ordinary differential equations corresponding to first-order conditions...
Research Article

6. On Lie Symmetry Analysis of Certain Coupled Fractional Ordinary Differential Equations

K. Sethukumarasamy, P. Vijayaraju, P. Prakash
Pages: 219 - 241
In this article, we explain how to extend the Lie symmetry analysis method for n-coupled system of fractional ordinary differential equations in the sense of Riemann-Liouville fractional derivative. Also, we systematically investigated how to derive Lie point symmetries of scalar and coupled fractional...
Research Article

7. Lie Symmetries of the Canonical Connection: Codimension One Abelian Nilradical Case

Hassan Almusawa, Ryad Ghanam, Gerard Thompson
Pages: 242 - 253
This paper studies the canonical symmetric connection ∇ associated to any Lie group G. The salient properties of ∇ are stated and proved. The Lie symmetries of the geodesic system of a general linear connection are formulated. The results are then applied to ∇ in the special case where the Lie algebra...
Research Article

8. Statistical de Rham Hodge Operators and the Kastler-Kalau-Walze Type Theorem for Manifolds With Boundary

Sining Wei, Yong Wang
Pages: 254 - 275
In this paper, we give the Lichnerowicz type formulas for statistical de Rham Hodge operators. Moreover, Kastler-Kalau-Walze type theorems for statistical de Rham Hodge operators on compact manifolds with (respectively without) boundary are proved.