Saturday, October 13, 2012: 2:00 PM
Hall 4E/F (WSCC)
A method to construct explicit solutions for Schroedinger
equations with quadratic time dependent Hamiltonian had been
introduced by one of the authors (ES) and coauthors (Cordero, Lopez
and Suslov) in 2008. Recently, Suazo and Suslov have use a
modification of the method to construct soliton-like solutions for
nonlinear Schroedinger equations with quadratic time-dependent
Hamiltonian their generality includes Gross-Pitavievskii (GP) equation
that it is believed models Bose-Einstein condensates phenomena. The
method mentioned before includes the study of solutions of the Riccati
equation with time dependent coefficients. In this project, we will
study numerical and analytical solutions of the Riccati equation with
time dependent coefficients and from these solutions derivate new
soliton-type solutions for GP equation.
equations with quadratic time dependent Hamiltonian had been
introduced by one of the authors (ES) and coauthors (Cordero, Lopez
and Suslov) in 2008. Recently, Suazo and Suslov have use a
modification of the method to construct soliton-like solutions for
nonlinear Schroedinger equations with quadratic time-dependent
Hamiltonian their generality includes Gross-Pitavievskii (GP) equation
that it is believed models Bose-Einstein condensates phenomena. The
method mentioned before includes the study of solutions of the Riccati
equation with time dependent coefficients. In this project, we will
study numerical and analytical solutions of the Riccati equation with
time dependent coefficients and from these solutions derivate new
soliton-type solutions for GP equation.