Applied asymptotic analysis

By Peter D. Miller. 2006

359 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/d104a2834fb1d2c1322f0b1d66e37b09f934bf95

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Citations in the corpus

Existence and Stability of a Two-Parameter Family of Solitary Waves for an NLS-KdV System (2012, background): “Discussions of the canonical nature of these equations may be found, for example, in chapters 13 and 17 of [23], chapter 2 of [20], or chapter 10 of [19].”
Lectures on non‐perturbative effects in large N gauge theories, matrix models and strings (2012, background): “Therefore, both saddles contribute to the asymptotics, which is then given by a linear combination of the two trans-series ZAi and ZBi (the precise combination can be obtained by a more detailed analysis, see [102]).”
Existence of global solutions to the derivative NLS equation with the inverse scattering transform method (2016, methodology): “We now add the condition u ∈ C1(R) and use the technique behind Watson’s Lemma related to the Laplace method of asymptotic analysis [27].”
The Horseshoe Estimator: Posterior Concentration around Nearly Black Vectors (2014, positive): “By a change of variables of x = 1 − z : R By following the proof of Watson’s lemma provided in Miller (2006), we can ﬁnd bounds on the numerator and denominator of the above expression.”
On the asymptotic magnitude of subsets of Euclidean space (2009, methodology): “which is what we will now derive using the classical asymptotic analysis technique known as Laplace’s method (see, for example, [9]).”
On the mean‐field limit for the consensus‐based optimization (2021, positive): “Furthermore, following similar arguments as in (12) and (13), one obtains”
Stochastic population dynamics in spatially extended predator–prey systems (2017, background): “ a multiscale expansion about the ensuing Hopf bifurcation [67, 68, 69]. Such an expansion is performed in terms of the ‘slow’ variables (X,T) = (ǫx, ǫ2t), where ǫ= p 3(µH − µ) is the small parameter [176]. The model’s complex Ginzburg Landau equation for the modulated amplitude A(X,T), which is a l”