Results 21 to 30 of about 2,922 (139)
Advances in High Energy Physics, Volume 2018, Issue 1, 2018., 2018 We examine the expansions of the solutions of the general Heun equation in terms of the Gauss hypergeometric functions. We present several expansions using functions, the forms of which differ from those applied before. In general, the coefficients of the expansions obey three‐term recurrence relations.
T. A. Ishkhanyan +3 more
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Cartan Prolongation of a Family of Curves Acquiring a Node [PDF]
, 2018 Using the monster/Semple tower construction, we study the structure of the Cartan prolongation of the family $x_1x_2 = t$ of plane curves with nodal central ...
Colley, Susan Jane, Kennedy, Gary
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Studies in Applied Mathematics, Volume 155, Issue 2, August 2025.ABSTRACT As part of the efforts aimed at extending Painlevé and Gambier's work on second‐order equations in one variable to first‐order ones in two, in 1981, Bureau classified the systems of ordinary quadratic differential equations in two variables which are free of movable critical points (which have the Painlevé Property).
Adolfo Guillot
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Singular Solutions to a (3 + 1)‐D Protter‐Morawetz Problem for Keldysh‐Type Equations
Advances in Mathematical Physics, Volume 2017, Issue 1, 2017., 2017 We study a boundary value problem for (3 + 1)‐D weakly hyperbolic equations of Keldysh type (problem PK). The Keldysh‐type equations are known in some specific applications in plasma physics, optics, and analysis on projective spaces. Problem PK is not well‐posed since it has infinite‐dimensional cokernel.
Nedyu Popivanov +4 more
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Stochastic Hydrodynamic Velocity Field and the Representation of Langevin Equations
Annalen der Physik, Volume 537, Issue 6, June 2025.A lumped method is proposed to account for both mean‐field hydrodynamics and stochastic fluctuations within the kinematic equations of motion, providing a regularized formulation of the overdamped approximation. The concept of stochastic realizability in broad sense is introduced based on the spectral properties of the Fredholm operator associated with
Massimiliano Giona +2 more
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Advances in Mathematical Physics, Volume 2017, Issue 1, 2017., 2017 A complete family of solutions for the one‐dimensional reaction‐diffusion equation, uxx(x, t) − q(x)u(x, t) = ut(x, t), with a coefficient q depending on x is constructed. The solutions represent the images of the heat polynomials under the action of a transmutation operator.
Vladislav V. Kravchenko +3 more
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Journal of Geophysical Research: Planets, Volume 130, Issue 4, April 2025.Abstract Certain spiral density waves in Saturn's rings are generated through resonances with planetary normal modes, making them valuable probes of Saturn's internal structure. Previous research has primarily focused on the rotation rates of these waves. However, other characteristics of these waves also contain valuable information about the planet's
V. M. Afigbo +6 more
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Construction of the Global Solutions to the Perturbed Riemann Problem for the Leroux System
Advances in Mathematical Physics, Volume 2016, Issue 1, 2016., 2016 The global solutions of the perturbed Riemann problem for the Leroux system are constructed explicitly under the suitable assumptions when the initial data are taken to be three piecewise constant states. The wave interaction problems are widely investigated during the process of constructing global solutions with the help of the geometrical structures
Pengpeng Ji, Chun Shen, Ming Mei
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A uniqueness theorem for a goursat-type problem
Applied Mathematics Letters, 1992 Consider the problem (1) \(u_{tt}- \Delta u+ q(x)u=0\), \(x\in\mathbb{R}^ 3\), \(-r\leq t\leq r\), \(r=| x|\), (2) \(u=0\) at \(t=\pm r\), \[ \varliminf_{R\to\infty} \int_{| s|=R} \int_{-R}^ R | u_ r\mp u_ t|^ 2 dt ds=0.\tag{3} \] The boundary data are given on the characteristic cone \(t=\pm r\). Condition (3) is a condition at infinity. Assume that \(
Mishnaevskii, P.A., Ramm, A.G.
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An Approach to Solve Fuzzy Fractional Darboux Problems Under the Caputo Derivative
International Journal of Differential Equations, Volume 2025, Issue 1, 2025.This paper investigates the Fuzzy Adomian Decomposition Method to find approximate analytical solutions for linear and nonlinear fuzzy Darboux problems using the Caputo‐type mixed fractional derivative, which plays an important role in applied and engineering sciences. The solutions are formulated as series with easily calculable terms.
Nagwa A. Saeed +2 more
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