The Experts below are selected from a list of 6789 Experts worldwide ranked by ideXlab platform
Francesco Oliveri - One of the best experts on this subject based on the ideXlab platform.
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on the Equations of ideal gas dynamics with a Separable Equation of state lie group analysis and substitution principles
International Journal of Non-linear Mechanics, 1992Co-Authors: Francesco OliveriAbstract:Abstract In this paper we consider the Equations that govern the flow of an inviscid, thermally non-conducting fluid with a Separable Equation of state within the theoretical framework of Lie group analysis. We show that the result known in the literature as the substitution principle can be derived by suitably imposing the invariance of the basic Equations under a one-parameter Lie group of transformations. Moreover, we prove that the use of the Lie group approach leads to different generalizations of the substitution principle.
Zensho Yoshida - One of the best experts on this subject based on the ideXlab platform.
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irregular modulation of non linear alfven beltrami wave coupled with an ion sound wave
Communications in Nonlinear Science and Numerical Simulation, 2014Co-Authors: S Emoto, Zensho YoshidaAbstract:Abstract A singularity of a system of differential Equations may produce “intrinsic” solutions that are independent of initial or boundary conditions—such solutions represent “irregular behavior” uncontrolled by external conditions. In the recently formulated non-linear model of Alfven/Beltrami waves [Commum Nonlinear Sci Numer Simulat 17 (2012) 2223], we find a singularity occurring at the resonance of the Alfven velocity and sound velocity, from which pulses bifurcate irregularly. By assuming a stationary waveform, we obtain a sufficient number of constants of motion to reduce the system of coupled ordinary differential Equations (ODEs) into a single Separable ODE that is readily integrated. However, there is a singularity in the Separable Equation that breaks the Lipschitz continuity, allowing irregular solutions to bifurcate. Apart from the singularity, we obtain solitary wave solutions and oscillatory solutions depending on control parameters (constants of motion).
Araya Wiwatwanich - One of the best experts on this subject based on the ideXlab platform.
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characterization of a nonlinear second order ode reducible to a Separable Equation
Burapha Science Journal (วารสารวิทยาศาสตร์บูรพา ), 2017Co-Authors: Pornthip Kasempin, Sujinan Chinated, Araya WiwatwanichAbstract:This paper aims to investigate the characteristics of a second order nonlinear ordinary differential Equation in the form which is reducible to a Separable Equation. In this regard, partial differentiation is the main tool for the reduction process. The main result reveals that “if the second order Equation above can be reduced to , where is a function of and is a function of , then ” Keywords : nonlinear ordinary differential Equations, Separable Equations
S Emoto - One of the best experts on this subject based on the ideXlab platform.
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irregular modulation of non linear alfven beltrami wave coupled with an ion sound wave
Communications in Nonlinear Science and Numerical Simulation, 2014Co-Authors: S Emoto, Zensho YoshidaAbstract:Abstract A singularity of a system of differential Equations may produce “intrinsic” solutions that are independent of initial or boundary conditions—such solutions represent “irregular behavior” uncontrolled by external conditions. In the recently formulated non-linear model of Alfven/Beltrami waves [Commum Nonlinear Sci Numer Simulat 17 (2012) 2223], we find a singularity occurring at the resonance of the Alfven velocity and sound velocity, from which pulses bifurcate irregularly. By assuming a stationary waveform, we obtain a sufficient number of constants of motion to reduce the system of coupled ordinary differential Equations (ODEs) into a single Separable ODE that is readily integrated. However, there is a singularity in the Separable Equation that breaks the Lipschitz continuity, allowing irregular solutions to bifurcate. Apart from the singularity, we obtain solitary wave solutions and oscillatory solutions depending on control parameters (constants of motion).
Robert E. O'malley - One of the best experts on this subject based on the ideXlab platform.
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NAIVE SINGULAR PERTURBATION THEORY
Mathematical Models and Methods in Applied Sciences, 2001Co-Authors: Robert E. O'malleyAbstract:The paper demonstrates, via extremely simple examples, the shocks, spikes, and initial layers that arise in solving certain singularly perturbed initial value problems for first-order ordinary differential Equations. As examples from stability theory, they are basic to many asymptotic techniques. First, we note that limiting solutions of linear homogeneous Equations on t≥0 are specified by the zeros of , rather than by the turning points where a(t) becomes zero. Furthermore, solutions to the solvable Equations for k=1, 2 or 3 can feature canards, where the trivial limit continues to apply after it becomes repulsive. Limiting solutions of the Separable Equation may likewise involve switchings between the zeros of c(x) located immediately above and below x(0), if they exist, at zeros of A(t). Finally, limiting solutions of many other problems follow by using asymptotic expansions for appropriate special functions. For example, solutions of can be given in terms of the Bessel functions Kj(t4/4e) and Ij(t4/4e) for j=3/8 and -5/8.
