General Euler-Poisson-Darboux Equation and Hyperbolic B-Potentials
نویسندگان
چکیده
منابع مشابه
The Euler-poisson-darboux Equation in the Exceptional Cases1
where in the EPD equation (1.1) it is understood that Aw = 2Zf=i «*,•*< and k is a parameter, — °° < k < °°. We designate a solution of Li[w]=0 by um(x, t), writing x in place of *i, ■ • • , xm. While particular results for this famous equation go back to Poisson and even to Euler, a systematic investigation of the Cauchy problem covering all values of k and m is of recent date. The results may...
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We find a remarkable subalgebra of higher symmetries of the elliptic Euler-Darboux equation. To this aim we map such equation into its hyperbolic analogue already studied by Shemarulin. Taking into consideration how symmetries and recursion operators transform by this complex contact transformation, we explicitly give the structure of this Lie algebra and prove that it is finitely generated. Fu...
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The Cauchy problem and the initial-boundary value problem for the Euler-Poisson system have been extensively investigated, together with a study of scaled and unscaled asymptotic limits. The pressure-density relationships employed have included both the adiabatic (isentropic) relation as well as the ideal gas law (isothermal). The study most closely connected to this one is that of S. Nishibata...
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n this paper, we apply Picard’s Iteration Method followed by Adomian Decomposition Method to solve a nonlinear Singular Cauchy Problem of Euler- Poisson- Darboux Equation. The solution of the problem is much simplified and shorter to arriving at the solution as compared to the technique applied by Carroll and Showalter (1976)in the solution of Singular Cauchy Problem.
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allowed for determined boundary conditions corresponding to the standard potential . With the very useful Darboux transformation (DT) [3-6] is possible to generalize any specific standard potential and thus generate new interaction models with the same energy levels. The DT is related to the Sturm-Liouville theory [7-10], and it is easy to see the implicit presence of DT in supersymmetric quant...
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ژورنال
عنوان ژورنال: Contemporary Mathematics. Fundamental Directions
سال: 2019
ISSN: 2413-3639
DOI: 10.22363/2413-3639-2019-65-2-157-338