Solution of the differential equation \((\partial^2/\partial x \partial y + ax \partial/\partial x + by \partial/\partial y +cxy+ \partial/\partial t) P (x,y,t)=0\) and the Bogoliubov transformation

DOI10.1016/0022-247X(73)90268-0zbMath0259.35070WikidataQ115364666 ScholiaQ115364666MaRDI QIDQ2560387

Publication date: 1973

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Series solutions to PDEs (35C10) Partial differential equations of mathematical physics and other areas of application (35Q99) Linear higher-order PDEs (35G05)

Cites Work

On a Hilbert space of analytic functions and an associated integral transform part I
Solution of the Differential Equation (∂2∂x∂y+ax∂∂x+by∂∂y+cxy+∂∂t)P=0
Closed-Form Solution of the Differential Equation (∂2∂x∂y+ax∂∂x+by ∂∂y+cxy+∂∂t)P=0 Subject to the Initial Condition P(x, y, t = 0) = Φ(x, y)
Exponential Operators and Parameter Differentiation in Quantum Physics
Solution of the Differential Equation (∂2∂x∂y+ax∂∂x+by∂∂y+cxy+∂∂t)P=0 Subject to the Initial Condition P(x,y,0)=Φ(x,y)
Closed-Form Solution of the Differential Equation (∂2∂x∂y+ax∂∂x+by∂∂y+cxy+∂∂t)P=0 by Normal-Ordering Exponential Operators
Initial-Value Problem for the Equation(∂∂t + a(t,x,y)∂∂x + b(t,x,y)∂∂y + c(t,x,y) + d(t,x,y)∂2∂x∂y)u=f(t,x,y) in the Complex Domain
On the Solution of the Differential Equation (∂2∂x∂y+ax∂∂x+by∂∂y+cxy+∂∂t)P=0

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