Advanced Search

We solve the operator equations $$\sum _{i=0}^n{a}_i(x)L\left[x^{n-i}\phi (x)\right]=0\mathit{\hspace{1em}}\text{and}\mathit{\hspace{1em}}\sum _{i=0}^n{a}_i(x)L\left[x^{n-i}\phi (x)\right]=A\left[\phi (x)\right],$$ where the unknown is the linear operator $L$, and obtain the solutions in three equivalent forms: as infinite-order differential operators with variable coefficients, as "translation" operators and as integral operators.

The main topic of this paper is the interaction between vortex density waves and high-frequency second sound in counterflow superfluid turbulence. To this end a thermodynamical model including vortex flux as independent variable is considered. This choice is crucial for the study of the transition of the behavior of the vortex-density perturbations from diffusive to propagative, which is necessary to interpret the details of the high-frequency second sound waves.