Publication Date
2007
Journal or Book Title
Mathematics and Computers in Simulation
Abstract
We demonstrate the systematic derivation of a class of discretizations of nonlinear Schrödinger (NLS) equations for general polynomial nonlinearity whose stationary solutions can be found from a reduced two-point algebraic condition. We then focus on the cubic problem and illustrate how our class of models compares with the well-known discretizations such as the standard discrete NLS equation, or the integrable variant thereof. We also discuss the conservation laws of the derived generalizations of the cubic case, such as the lattice momentum or mass and the connection with their corresponding continuum siblings.
Pages
343-351
Volume
74
Issue
4-5
Recommended Citation
Kevrekidis, PG, "On a class of spatial discretizations of equations of the nonlinear Schrödinger type" (2007). Mathematics and Computers in Simulation. 1084.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/1084
Comments
This is the pre-published version harvested from arXiv. The published version is located at http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V0T-4MFTVMW-3&_user=1516330&_coverDate=03%2F30%2F2007&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_searchStrId=1581609448&_rerunOrigin=google&_acct=C000053443&_version=1&_urlVersion=0&_userid=1516330&md5=23b6a98ecd173c0d7c1a3f02252a4275&searchtype=a