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The existence of localized solution requires that the Sagdeev potential have a maximum value at the origin, viz.
We find an exact analytical family of nondiffracting localized solution.
The image shows two realities juxtaposed against one another where Ayala depicts a localized solution dependent on microeconomic transactions while the red to dead conveyance commentary is a possible consequence of a mega-scale investment.
However, in case of a localized solution, cavitation follows the formation of the shear band, with the two events being quite distinct.
The model was originally designed to have a stable localized solution for a range of parameters as a consequence of the coexistence of a stable limit cycle and a stable fixed point.
In this paper an efficient and accurate method for simulating the propagation of a localized solution of the Schrödinger equation with a smooth potential near the semiclassical limit is presented.
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Localized solutions best solve local problems.
Based on John Burke and Edgar Knobloch's work we conclude preliminarily that the equation will have localized solutions.
I present broad implications for a paradigm shift away from the dominant large-scale energy infrastructure as a means of energy security discourse, toward a more encompassing security agenda that considers distributed and localized solutions.
Of particular interest is the ability of the method to capture the highly localized, transient solution in the vicinity of a heat source or material interface.
The goal is to find a linear combination, w, of the ensemble solutions to minimize the cost function (13) J * (w ) = (k - 1 ) w T w + [ y o - y ¯ b - y b w ] T R - 1 [ y o - y ¯ b - y b w ], which is the analogue of Eq. (10) in the subspace spanned by the spatially localized ensemble solutions [ 17].
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