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We present a time-local existence theorem of solutions to the initial value problem for a third-order dispersive evolution equation for open curves into compact almost Hermitian manifolds. Our equatio...ns geometrically generalize a two-sphere valued physical model describing the motion of vortex filament. These equations cause the so-called loss of one-derivative since the target manifold is not supposed to be a Kähler manifold. We overcome this difficulty by using a gauge transformation of a multiplier on the pull-back bundle to eliminate the bad first order terms essentially.続きを見る
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Mendeley出力
