The Discrete Nonlinear Schrödinger Equation and its Lie Symmetry Reductions
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The Lie algebra L(h) of symmetries of a discrete analogue of the non-linear Schrödinger equation (NLS) is studied. A five-dimensional subspace of L(h), generated by both point and generalized symmetries, transforms into the five-dimensional point symmtry algebra L(0) of the NLS equation. We use the lowest symmetries to do symmetry reduction of the equation, thus obtaining explicit solutions and discrete analogues of elliptic functions.
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Cite this article
TY - JOUR AU - R. Hernández Heredero AU - D. Levi PY - 2003 DA - 2003/12/01 TI - The Discrete Nonlinear Schrödinger Equation and its Lie Symmetry Reductions JO - Journal of Nonlinear Mathematical Physics SP - 77 EP - 94 VL - 10 IS - Supplement 2 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.2003.10.s2.6 DO - 10.2991/jnmp.2003.10.s2.6 ID - Heredero2003 ER -