Hamiltonian Integration Method for Nonlinear Schroedinger Equation
Start Date
8-11-2017 1:30 PM
End Date
8-11-2017 5:30 PM
Abstract
The nonlinear Schroedinger equations (NLSE) are used to study different physical phenomena such as dynamics of water waves, Langmuir waves in hot plasmas, and light pulses propagation in fiber optics. Different methods can be used to solve these equations numerically. We compare second order split-step method and Hamiltonian integration method introduced in 1992 by Dyachenko et al. In order to test these methods, we use focusing one dimensional NLSE which together with trivial integrals of motion (e.g. the Hamiltonian and wave action) allows us to study conservation of nontrivial integrals of motion. Conservation of nontrivial integrals of motion shows whether a numerical method violates the integrability of the system significantly.
Hamiltonian Integration Method for Nonlinear Schroedinger Equation
The nonlinear Schroedinger equations (NLSE) are used to study different physical phenomena such as dynamics of water waves, Langmuir waves in hot plasmas, and light pulses propagation in fiber optics. Different methods can be used to solve these equations numerically. We compare second order split-step method and Hamiltonian integration method introduced in 1992 by Dyachenko et al. In order to test these methods, we use focusing one dimensional NLSE which together with trivial integrals of motion (e.g. the Hamiltonian and wave action) allows us to study conservation of nontrivial integrals of motion. Conservation of nontrivial integrals of motion shows whether a numerical method violates the integrability of the system significantly.
