On the one-dimensional cubic nonlinear Schrodinger equation below L^2 [PDF]
, 2010 In this paper, we review several recent results concerning well-posedness of the one-dimensional, cubic Nonlinear Schrodinger equation (NLS) on the real line R and on the circle T for solutions below the L^2-threshold. We point out common results for NLS
Oh, Tadahiro, Sulem, Catherine
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Comparing the stochastic nonlinear wave and heat equations: a case study [PDF]
, 2020 We study the two-dimensional stochastic nonlinear wave equation (SNLW) and stochastic nonlinear heat equation (SNLH) with a quadratic nonlinearity, forced by a fractional derivative (of order $\alpha > 0$) of a space-time white noise.
Oh, Tadahiro, Okamoto, Mamoru
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The Painleve Test and Reducibility to the Canonical Forms for Higher-Dimensional Soliton Equations with Variable-Coefficients [PDF]
, 2006 The general KdV equation (gKdV) derived by T. Chou is one of the famous (1+1) dimensional soliton equations with variable coefficients. It is well-known that the gKdV equation is integrable.
Kobayashi, Tadashi, Toda, Kouichi
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On a Whitham-Type Equation [PDF]
, 2009 The Hunter-Saxton equation and the Gurevich-Zybin system are considered as two mutually non-equivalent representations of one and the same Whitham-type equation, and all their common solutions are obtained ...
Sakovich, Sergei
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Deep quench approximation and optimal control of general Cahn-Hilliard systems with fractional operators and double obstacle potentials [PDF]
, 2018 The paper arXiv:1804.11290 contains well-posedness and regularity results for a system of evolutionary operator equations having the structure of a Cahn-Hilliard system.
Colli, Pierluigi +2 more
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Lie symmetries of a third order PDE system [PDF]
arXiv, 2021 In this paper we show that a third order PDE system that is a general form of a CR-geometry PDE system has at most a ten-dimensional Lie symmetry algebra. We also show that this estimate is precise.
arxiv
A remark on normal forms and the "upside-down" I-method for periodic NLS: growth of higher Sobolev norms [PDF]
, 2011 We study growth of higher Sobolev norms of solutions to the one-dimensional periodic nonlinear Schrodinger equation (NLS). By a combination of the normal form reduction and the upside-down I-method, we establish \|u(t)\|_{H^s} \lesssim (1+|t|)^{\alpha (s-
Colliander, James +2 more
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Complex plane representations and stationary states in cubic and quintic resonant systems
, 2019 Weakly nonlinear energy transfer between normal modes of strongly resonant PDEs is captured by the corresponding effective resonant systems. In a previous article, we have constructed a large class of such resonant systems (with specific representatives ...
Biasi, Anxo, Bizon, Piotr, Evnin, Oleg
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Solvable cubic resonant systems
, 2019 Weakly nonlinear analysis of resonant PDEs in recent literature has generated a number of resonant systems for slow evolution of the normal mode amplitudes that possess remarkable properties.
Biasi, Anxo, Bizon, Piotr, Evnin, Oleg
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Exponential decay properties of a mathematical model for a certain fluid-structure interaction
, 2014 In this work, we derive a result of exponential stability for a coupled system of partial differential equations (PDEs) which governs a certain fluid-structure interaction.
Avalos, George, Bucci, Francesca
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