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Instability of the finite‐difference split‐step method applied to the generalized nonlinear Schrödinger equation. III. external potential and oscillating pulse solutions 下载免费PDF全文
Taras I. Lakoba 《Numerical Methods for Partial Differential Equations》2017,33(3):633-650
This is the final part of a series of articles where we have studied numerical instability (NI) of localized solutions of the generalized nonlinear Schrödinger equation (gNLS). It extends our earlier studies of this topic in two ways. First, it examines differences in the development of the NI between the case of the purely cubic NLS and the case where the gNLS has an external bounded potential. Second, it investigates how the NI is affected by the oscillatory dynamics of the simulated pulse. The latter situation is common when the initial condition is not an exact stationary soliton. We have found that in this case, the NI may remain weak when the time step exceeds the threshold quite significantly. This means that the corresponding numerical solution, while formally numerically unstable, can remain sufficiently accurate over long times, because the numerical noise will stay small. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 633–650, 2017 相似文献
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We study algebraic and topological properties of the convolution semigroup of probability measures on a topological groups
and show that a compact Clifford topological semigroup S embeds into the convolution semigroup P(G) over some topological group G if and only if S embeds into the semigroup exp(G)\exp(G) of compact subsets of G if and only if S is an inverse semigroup and has zero-dimensional maximal semilattice. We also show that such a Clifford semigroup S embeds into the functor-semigroup F(G) over a suitable compact topological group G for each weakly normal monadic functor F in the category of compacta such that F(G) contains a G-invariant element (which is an analogue of the Haar measure on G). 相似文献
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Taras Radul 《Applied Categorical Structures》2011,19(4):729-739
Let
\mathbbF\mathbb{F} be a monad in the category Comp. We build for each
\mathbbF\mathbb{F}-algebra a convexity in general sense (see van de Vel 1993). We investigate properties of such convexities and apply them to prove that the multiplication map of the order-preserving
functional monad is soft. 相似文献
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N. A. Krasovskii A. M. Taras’ev 《Proceedings of the Steklov Institute of Mathematics》2010,269(1):174-185
We address the problem of optimal reconstruction of the values of a linear operator on ℝ
d
or ℤ
d
from approximate values of other operators. Each operator acts as the multiplication of the Fourier transform by a certain
function. As an application, we present explicit expressions for optimal methods of reconstructing the solution of the heat
equation (for continuous and difference models) at a given instant of time from inaccurate measurements of this solution at
other time instants. 相似文献
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Taras Skrypnyk 《Letters in Mathematical Physics》2017,107(5):793-819
We solve a problem of separation of variables for the classical integrable hamiltonian systems possessing Lax matrices satisfying linear Poisson brackets with the non-skew-symmetric, non-dynamical elliptic \(so(3)\otimes so(3)\)-valued classical r-matrix. Using the corresponding Lax matrices, we present a general form of the “separating functions” B(u) and A(u) that generate the coordinates and the momenta of separation for the associated models. We consider several examples and perform the separation of variables for the classical anisotropic Euler’s top, Steklov–Lyapunov model of the motion of anisotropic rigid body in the liquid, two-spin generalized Gaudin model and “spin” generalization of Steklov–Lyapunov model. 相似文献
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Taras Radul 《Applied Categorical Structures》2001,9(5):457-463
We introduce a class of Lawson monads and show that these monads have a functional representation. A characterisation of such a representation for the inclusion hyperspace monad is given. 相似文献