RICCATI EQUATION, FACTORIZATION METHOD AND SHAPE INVARIANCE

Riccati equation, Factorization Method and Shape Invariance

v 1 1 4 O ct 1 99 9 Riccati equation , Factorization Method and Shape Invariance

The basic concepts of factorizable problems in one–dimensional Quantum Mechanics, as well as the theory of Shape Invariant potentials are reviewed. The relation of this last theory with a generalization of the classical Factorization Method presented by Infeld and Hull is analyzed in detail. By the use of some properties of the Riccati equation the solutions of Infeld and Hull are greatly gener...

An Extended Riccati Equation Rational Expansion Method and its Applications

Based on computerized symbolic computation and a new general ansatz,an extended Riccati equation rational expansion method is presented to construct multiple exact solutions for nonlinear evolution equations and implemented in a computer algebraic system.The validity and reliability of the method are tested by its application to four nonlinear evolution equations arising in physics,namely,gener...

A Fast Newton's Method for a Nonsymmetric Algebraic Riccati Equation

A special instance of the algebraic Riccati equation XCX−XE−AX+B = 0 where the n × n matrix coefficients A,B,C,E are rank structured matrices is considered. Relying on the structural properties of Cauchy-like matrices, an algorithm is designed for performing the customary Newton iteration in O(n2) arithmetic operations (ops). The same technique is used to reduce the cost of the algorithm propos...

An Analytical Method for Solving General Riccati Equation

Abstract—In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be ...