Multiscale Analysis of Discrete Nonlinear Evolution Equations: The Reduction of the dNLS

References

• Ablowitz M.J. Ladik J.F. A nonlinear difference scheme and inverse scattering, Stud. Appl. Math. 55, (1976), 213–229
   Google Scholar
• Calogero F. What is Integrability, ed. Zakharov V. E., Springer, Berlin, 1991, 1–61; Calogero F. and Eckhaus W., Necessary conditions for integrability of nonlinear PDEs, Inv. Probl. 3, (1987), L27–L32
   Google Scholar
• Hernández Heredero R. Levi D. The Discrete Nonlinear Schrödinger Equation and its Lie symmetry reductions, Jour. Non. Math. Phys. 10, Suppl. 2, (2003), 77–94
   Google Scholar
• Hernández Heredero R. Levi D. Rodríguez M.A. Winternitz P. Lie Algebra Contractions and Symmetries of the Toda Hierarchy, J. Phys. A: Math. Gen. 33, (2000), 5025–5040
   Google Scholar
• Jordan C. Calculus of Finite Differences, Röttig and Romwalter, Sopron, 1939
   Google Scholar
• Leon J. Manna M. Multiscale analysis of discrete nonlinear evolution equations, J. Phys. A: Math. Gen. 32, (1999), 2845–2869
   Google Scholar
• Levi D. Yamilov R. Conditions for the existence of higher symmetries of evolutionary equations on the lattice, Jour. Math. Phys. 38, (1997), 6648–6674
   Google Scholar
• Levi D. Yamilov R. On the integrability of a new discrete nonlinear Schrödinger equation, J. Phys. A: Math. Gen. 34, (2001), L553–L562
   Google Scholar
• Sakovich S. Yu. Singularity analysis of a new discrete nonlinear Schrödinger equation, arXiv:nlin.SI/0111060, 28 Nov 2001
   Google Scholar
• Taniuti T. Reductive perturbation method and far fields of wave equations, Prog. Theor. Phys. Suppl. 55, (1974), 1–35
   Google Scholar
• Zhakarov V.E. Kuznetsov E.A. Multi-scale expansions in the theory of systems integrable by the inverse scattering transform, Physica 18D, (1986), 455–463
   Google Scholar