Journal of Nonlinear Mathematical Physics
1776-0852
Cơ quản chủ quản: Springer Nature , Springer International Publishing AG
Lĩnh vực:
Statistical and Nonlinear PhysicsMathematical Physics
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Các bài báo tiêu biểu
Symmetry Reductions of a Hamilton-Jacobi-Bellman Equation Arising in Financial Mathematics
Tập 12 Số 2 - Trang 268
On Linear and Non-Linear Representations of the Generalized Poincaré Groups in the Class of Lie Vector Fields
Tập 1 - Trang 295-308 - 1994
We study representations of the generalized Poincaré group and its extensions in the class of Lie vector fields acting in a space of n + m independent and one dependent variables. We prove that an arbitrary representation of the group P(n, m) with max {n, m} ≥ 3 is equivalent to the standard one, while the conformal group C (n, m) has non-trivial nonlinear representations. Besides that, we investigate in detail representations of the Poincaré group P (2, 2), extended Poincaré groups ̃P (1, 2), ̃P (2, 2), and conformal groups C (1, 2), C (2, 2) and obtain their linear and nonlinear representations.
Quantum Differential Forms
Tập 5 - Trang 245-288 - 1998
Formalism of differential forms is developed for a variety of Quantum and noncommutative situations.
Multicomplex solitons
Tập 27 - Trang 17-35 - 2019
We discuss integrable extensions of real nonlinear wave equations with multi-soliton solutions, to their bicomplex, quaternionic, coquaternionic and octonionic versions. In particular, we investigate these variants for the local and nonlocal Korteweg-de Vries equation and elaborate on how multi-soliton solutions with various types of novel qualitative behaviour can be constructed. Corresponding to the different multicomplex units in these extensions, real, hyperbolic or imaginary, the wave equations and their solutions exhibit multiple versions of antilinear or PT-symmetries. Utilizing these symmetries forces certain components of the conserved quantities to vanish, so that one may enforce them to be real. We find that symmetrizing the noncommutative equations is equivalent to imposing a PT-symmetry for a newly defined imaginary unit from combinations of imaginary and hyperbolic units in the canonical representation.
An RBF-FD Method for Numerical Solutions of 2D Diffusion-Wave and Diffusion Equations of Distributed Fractional Order
Tập 30 - Trang 1357-1374 - 2023
The subject of this paper is to propose a numerical algorithm for solving 2D diffusion and diffusion-wave equations of distributed order fractional derivatives. Such equations arise in modelling complex systems and have many important applications. Existence of integral term over the order of fractional derivative causes the high complexity of these equations and so their numerical solutions needs special cares. Using Gauss quadrature approach for discretizing the integral term of fractional derivative converts the distributed equation into a multi-term fractional differential equation. Then, the time variable is discretized with a suitable finite difference approach. The resultant semi-discretized equations are fully discretized by a radial basis function-generated finite difference based method. Convergence of the method are studied numerically. Various kind of test problems are considered for a comprehensive numerical study and the results confirm the efficiency of the method.
On a q-Difference Painlevé III Equation: I. Derivation, Symmetry and Riccati Type Solutions
Tập 10 Số 1 - Trang 86
Invariance Analysis of the (2+1) Dimensional Long Dispersive Wave Equation
Tập 4 - Trang 251-260 - 1997
In this paper, we bring out the Lie symmetries and associated similarity reductions of the recently proposed (2+1) dimensional long dispersive wave equation. We point out that the integrable system admits an infinite-dimensional symmetry algebra along with Kac-Moody-Virasoro-type subalgebras. We also bring out certain physically interesting solutions.