Constructing analytic solutions on the Tricomi equation

Analytic solutions of the Madelung equation

We present analytic self-similar solutions for the one, two and three dimensional Madelung hydrodynamical equation for a free particle. There is a direct connection between the zeros of the Madelung fluid density and the magnitude of the quantum potential. 1 ar X iv :1 70 3. 10 48 2v 1 [ qu an tph ] 3 0 M ar 2 01 7

On Analytic Solutions of the Equation (t ? )f() = X

Fundamental Solutions for the Tricomi Operator, Ii

In this paper we explicitly calculate fundamental solutions for the Tricomi operator, relative to an arbitrary point in the plane, and show that all such fundamental solutions originate from the hypergeometric function F (1/6, 1/6; 1; ζ) that is obtained when we look for homogeneous solutions to the reduced hyperbolic Tricomi equation.

Fundamental Solutions for the Tricomi Operator, Ii

In this paper we explicitly calculate fundamental solutions for the Tricomi operator, relative to an arbitrary point in the plane, and show that all such fundamental solutions originate from the hypergeometric function F(1/6, 1/6; 1; ζ ) that is obtained when we look for homogeneous solutions to the reduced hyperbolic Tricomi equation.

Analytic properties of matrix Riccati equation solutions

For matrix Riccati equations of platoontype systems and of systems arising from PDEs, assuming the coefficients are analytic functions in a suitable domain, the analyticity of the stabilizing solution is proved under various hypotheses. In addition, general results on the analytic behavior of stabilizing solutions are developed. I. NONSTANDARD RICCATI EQUATIONS In [10], [7] and elsewhere contin...