Analytic Solutions of the Madelung 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

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...

Analytic Solutions to Repulsive Nonlinear Schrödinger Equation

In this paper we make use of the the sn-ns method to obtain new exact solutions to so called repulsive or de-focusing nonlinear Schrödinger equation. These solutions are given in terms of Jacobi elliptic functions sn and ns.

Existence and Uniqueness of Analytic Solutions of the Shabat Equation

Sufficient conditions are given so that the initial value problem for the Shabat equation has a unique analytic solution, which, together with its first derivative, converges absolutely for z ∈ C : |z| < T , T > 0. Moreover, a bound of this solution is given. The sufficient conditions involve only the initial condition, the parameters of the equation, and T . Furthermore, from these conditions,...

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