Integral Representations of Partial Solutions for a Degenerate Third-Order Differential Equation

Annotatsiya

In the article, in the positive domain $$\Omega=\big{\{}(x,y,t):\,x>0,\,y>0,\,t>0\big{\}}$$ we consider a degenerate third-order differential equation of the form $$x^{n}y^{m}\,u_{t}=t^{k}y^{m}\,u_{xxx}+t^{k}x^{n}\,u_{yyy}$$ , $$m,n,k={\textrm{const}}>0$$ . Nine partial solutions of this equation are expressed through the Campe de Feriet hypergeometric functions $$F_{0;2;2}^{1;0,0}[x,y]$$ . By generalizing the operator method of J.L. Burchnall and T.W. Chaundy, one-dimensional reciprocal symbolic operators are introduced. Using Burchnall–Chaundy operators, decomposition formulas and integral representations for the Campe de Feriet hypergeometric function $$F_{0;2;2}^{1;0,0}[x,y]$$ are obtained.

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Identifikatorlar

DOI

10.1134/s199508022460033x

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