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The “good” Boussinesq equation : long-time asymptotics
Analysis & PDE, 2023 We consider the initial-value problem for the ``good'' Boussinesq equation on the line. Using inverse scattering techniques, the solution can be expressed in terms of the solution of a $3 \times 3$-matrix Riemann-Hilbert problem. We establish formulas for the long-time asymptotics of the solution by performing a Deift-Zhou steepest descent analysis of ...
Charlier, Christophe +2 more
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Long-Time Asymptotics of a Three-Component Coupled mKdV System
Mathematics, 2019 We present an application of the nonlinear steepest descent method to a three-component coupled mKdV system associated with a 4 × 4 matrix spectral problem. An integrable coupled mKdV hierarchy with three potentials is first generated. Based
Wen-Xiu Ma
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Long-time asymptotics for the short pulse equation [PDF]
Journal of Differential Equations, 2018 In this paper, we analyze the long-time behavior of the solution of the initial value problem (IVP) for the short pulse (SP) equation. As the SP equation is a complete integrable system, which posses a Wadati-Konno-Ichikawa (WKI)-type Lax pair, we formulate a $2\times 2$ matrix Riemann-Hilbert problem to this IVP by using the inverse scattering method.
exaly +4 more sources
Long-Time Asymptotics for Polymerization Models [PDF]
Communications in Mathematical Physics, 2018 https://link.springer.com/article/10.1007/s00220-018-3218 ...
Calvo, Juan +2 more
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Long Time Asymptotics for Optimal Investment [PDF]
, 2015 This survey reviews portfolio selection problem for long-term horizon. We consider two objectives: (i) maximize the probability for outperforming a target growth rate of wealth process (ii) minimize the probability of falling below a target growth rate. We study the asymptotic behavior of these criteria formulated as large deviations control pro\-blems,
Rosenbaum, M., Yor, Marc
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Long-time Asymptotics for the Camassa–Holm Equation [PDF]
SIAM Journal on Mathematical Analysis, 2009 We apply the method of nonlinear steepest descent to compute the long-time asymptotics of the Camassa-Holm equation for decaying initial data, completing previous results by A. Boutet de Monvel and D. Shepelsky.
Anne Boutet de Monvel +3 more
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Long-Time Asymptotics for the Nonlocal MKdV Equation* [PDF]
Communications in Theoretical Physics, 2019 Abstract In this paper, we study the Cauchy problem with decaying initial data for the nonlocal modified Korteweg-de Vries equation (nonlocal mKdV) q t (x, t) + q xxx (x,t) −6q(x, t)q(−x, −t)q
He, Feng-Jing, Fan, En-Gui, Xu, Jian
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The asymptotics of stochastically perturbed reaction-diffusion equations and front propagation
Comptes Rendus. Mathématique, 2020 We study the asymptotics of Allen–Cahn-type bistable reaction-diffusion equations which are additively perturbed by a stochastic forcing (time white noise).
Lions, Pierre-Louis +1 more
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THE ASYMPTOTICS OF A SOLUTION OF THE MULTIDIMENSIONAL HEAT EQUATION WITH UNBOUNDED INITIAL DATA
Ural Mathematical Journal, 2021 For the multidimensional heat equation, the long-time asymptotic approximation of the solution of the Cauchy problem is obtained in the case when the initial function grows at infinity and contains logarithms in its asymptotics.
Sergey V. Zakharov
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ON THE LONG-TIME ASYMPTOTICS OF QUANTUM DYNAMICAL SEMIGROUPS [PDF]
Quantum Probability and Related Topics, 2011 We consider semigroups $\{α_t: \; t\geq 0\}$ of normal, unital, completely positive maps $α_t$ on a von Neumann algebra ${\mathcal M}$. The (predual) semigroup $ν_t (ρ):= ρ\circ α_t$ on normal states $ρ$ of $\mathcal M$ leaves invariant the face ${\mathcal F}_p:= \{ρ: \; ρ(p)=1\}$ supported by the projection $p\in {\mathcal M}$, if and only if $α_t(p ...
Raggio, Guido A., Zangara, Pablo R.
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