Weierstrass’ Elliptic Function Solution to the Autonomous Limit of the String Equation of Type (2,5)*

Abstract

In this article, we study the string equation of type (2,5), which is derived from 2D gravity theory or the string theory. We consider the equation as a 4th order analogue of the first Painlevé equation, take the autonomous limit, and solve it concretely by use of the Weierstrass' elliptic function.

Weierstrass’ Elliptic Function Solutions to the Autonomous Limit of the String Equation

“…Theorem E [17]. For suitable 2 ( , ) a b ∈  , the autonomous Equation (9) has a solution concretely described as ( ) ( ),3 ( ).…”