Motion of an integral curve of a Hamiltonian dynamical system and the evolution equations in 3D
2017 ◽
Vol 14
(12)
◽
pp. 1750172
Keyword(s):
We show that all of the nonstretching curve motions specified in the Frenet–Serret frame in the literature can be described by the time evolution of an integral curve of a Hamiltonian dynamical system such that the underlying curve is a geodesic curve on a leaf of the foliation determined by the Poisson structure in three dimensions. As an illustrative example, we show that the focusing version of the nonlinear Schrödinger equation and the complex modified Korteweg–de Vries (mKdV) equation are obtained in this way.
2018 ◽
Vol 33
(14n15)
◽
pp. 1850085
Keyword(s):
Keyword(s):
2020 ◽
Vol 34
(29)
◽
pp. 2050282