Inhomogeneous Burgers Equation and the Feynman-Kac Path Integral

Details Inhomogeneous Burgers Equation and the Feynman-Kac Path Integral Inhomogeneous Burgers Equation and the Feynman-Kac Path Integral

1998-12-15

arxiv.org/abs/solv-int/9812014v1

Physics

High Energy Physics

High Energy Physics - Theory

12 pages

Scientific paper

By linearizing the inhomogeneous Burgers equation through the Hopf-Cole transformation, we formulate the solution of the initial value problem of the corresponding linear heat type equation using the Feynman-Kac path integral formalism. For illustration, we present the exact solution for the forcing term of the form: $F(x,t)=\omega ^2x+f(t).$ We also present the initial value problem solution for the case with a constant forcing term to compare with the known result.

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