SYMPLECTIC NUMERICAL METHODS IN DYNAMICS OF NONLINEAR WAVES
1999 ◽
Vol 10
(05)
◽
pp. 967-980
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Keyword(s):
The symplectic integrator of the Gauss–Legendre type is tested on the nonlinear Schrödinger equation. Preservation of high integrals (up to 10 or more) and quasiperiodic motion have been detected for dynamics on both stable soliton and homoclinic manifolds, which indicate applicability of symplectic integrators for adequate simulation of integrable equation. The tested integrator is applied to the problem of long-time stability of the solitons in higher-derivative nonlinear Schrödinger equation. The slow logarithmic-type depletion of the soliton amplitude with time has been detected.
2021 ◽
pp. 272-304
2013 ◽
Vol 16
(3)
◽
pp. 253-288
◽
2014 ◽
Vol 378
(26-27)
◽
pp. 1809-1815
◽
2018 ◽
Vol 35
(1)
◽
pp. 217-265
◽
2021 ◽
Vol 382
(1)
◽
pp. 87-121