Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2006-03-23
Nonlinear Sciences
Exactly Solvable and Integrable Systems
Submitted for publication in a journal on October 14, 2005
Scientific paper
We demonstrate the systematic derivation of a class of discretizations of nonlinear Schr{\"o}dinger (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.
Dmitriev Sergey V.
Kevrekidis Panagiotis G.
Sukhorukov Andrey A.
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