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Bright vector solitons in cross-defocusing nonlinear media
vector solitons cross-defocusing nonlinear media
2010/4/2
We study two-dimensional soliton-soliton vector pairs in media with self-focusing nonlinearities and defocing cross-interactions. The general properties of the stationary states and their stability ar...
KdV solitons in Einstein's vacuum field equations
KdV solitons Kortweg-de Vries Einstein's vacuum field equations
2010/4/2
We present a metric for which Einstein's field equations in vacuum generate the Kortweg-de Vries (KdV) equation and thus its $N$-soliton solutions solve the vacuum equations. The metric of the one sol...
The relations between smooth and peaked soliton solutions are reviewed for the Camassa-Holm (CH) shallow water wave equation in one spatial dimension. The canonical Hamiltonian formulation of the CH e...