Invariant Manifolds of Traveling Waves of the 3D Gross–Pitaevskii Equation in the Energy Space

[1]  D. Chiron,et al.  Traveling Waves for Nonlinear Schrödinger Equations with Nonzero Conditions at Infinity , 2017, Archive for Rational Mechanics and Analysis.

[2]  Chongchun Zeng,et al.  Stability of Traveling Waves of Nonlinear Schrödinger Equation with Nonzero Condition at Infinity , 2014, 1405.2583.

[3]  K. Nakanishi,et al.  Center-stable manifold of the ground state in the energy space for the critical wave equation , 2013, 1303.2400.

[4]  D. Chiron,et al.  Rarefaction Pulses for the Nonlinear Schrödinger Equation in the Transonic Limit , 2012, 1210.1315.

[5]  K. Nakanishi,et al.  Threshold Phenomenon for the Quintic Wave Equation in Three Dimensions , 2012, 1209.0347.

[6]  M. Beceanu A critical center‐stable manifold for Schrödinger's equation in three dimensions , 2012 .

[7]  Kenji Nakanishi,et al.  Invariant Manifolds Around Soliton Manifolds for the Nonlinear Klein-Gordon Equation , 2011, SIAM J. Math. Anal..

[8]  K. Nakanishi,et al.  Global dynamics above the ground state energy for the one-dimensional NLKG equation , 2010, 1011.1776.

[9]  K. Nakanishi,et al.  Global Dynamics Above the Ground State for the Nonlinear Klein–Gordon Equation Without a Radial Assumption , 2010, 1011.0132.

[10]  K. Nakanishi,et al.  Global dynamics above the ground state energy for the cubic NLS equation in 3D , 2010, Calculus of Variations and Partial Differential Equations.

[11]  J. Saut,et al.  Existence and properties of travelling waves for the Gross-Pitaevskii equation , 2009, 0902.3804.

[12]  David Chiron,et al.  Traveling Waves for Nonlinear Schrödinger Equations with Nonzero Conditions at Infinity , 2012, Archive for Rational Mechanics and Analysis.

[13]  Peter W. Bates,et al.  Approximately invariant manifolds and global dynamics of spike states , 2008 .

[14]  Jean-Claude Saut,et al.  Travelling Waves for the Gross-Pitaevskii Equation II , 2007, 0711.2408.

[15]  Patrick Gérard,et al.  The Cauchy problem for the Gross-Pitaevskii equation , 2006 .

[16]  K. Nakanishi,et al.  Global Dispersive Solutions for the Gross–Pitaevskii Equation in Two and Three Dimensions , 2006, math/0605655.

[17]  Wilhelm Schlag,et al.  Stable manifolds for all monic supercritical focusing nonlinear Schrödinger equations in one dimension , 2006 .

[18]  Philippe Gravejat Decay for travelling waves in the Gross–Pitaevskii equation , 2004 .

[19]  N. Berloff,et al.  Motions in a Bose condensate: X. New results on the stability of axisymmetric solitary waves of the Gross-Pitaevskii equation , 2004, cond-mat/0407482.

[20]  David Chiron,et al.  Travelling waves for the Gross-Pitaevskii equation in dimension larger than two. , 2004 .

[21]  Giandomenico Orlandi,et al.  Vortex rings for the Gross-Pitaevskii equation , 2004 .

[22]  Caroline Nore,et al.  Gross–Pitaevskii dynamics of Bose–Einstein condensates and superfluid turbulence , 2003 .

[23]  Philippe Gravejat,et al.  A Non-Existence Result for Supersonic Travelling Waves in the Gross-Pitaevskii Equation , 2003 .

[24]  Yue Liu,et al.  Strong instability of solitary-wave solutions to a Kadomtsev-Petviashvili equation in three dimensions , 2002 .

[25]  Shui-Nee Chow,et al.  Center manifolds for smooth invariant manifolds , 2000 .

[26]  F. Gesztesy,et al.  A Spectral Mapping Theorem and Invariant Manifolds for Nonlinear Schr , 1999, solv-int/9907017.

[27]  Shui-Nee Chow,et al.  Smoothness of inertial manifolds , 1992 .

[28]  J. Shatah,et al.  Stability theory of solitary waves in the presence of symmetry, II☆ , 1990 .

[29]  I. V. Barashenkov,et al.  Soliton-like “bubbles” in a system of interacting bosons , 1988 .

[30]  P H Roberts,et al.  Motions in a Bose condensate. V. Stability of solitary wave solutions of non-linear Schrodinger equations in two and three dimensions , 1986 .

[31]  Paul H. Roberts,et al.  Motions in a Bose condensate: IV. Axisymmetric solitary waves , 1982 .

[32]  P H Roberts,et al.  Motions in a Bose condensate. III. The structure and effective masses of charged and uncharged impurities , 1974 .

[33]  Wilhelm Schlag,et al.  Stable manifolds for an orbitally unstable nonlinear Schrödinger equation , 2009 .

[34]  M. Beceanu A Centre-Stable Manifold for the Focussing Cubic NLS in R 1+3 , 2007 .

[35]  Peter W. Bates,et al.  Invariant Manifolds for Semilinear Partial Differential Equations , 1989 .

[36]  I. V. Barashenkov,et al.  Stability of the soliton-like “bubbles” , 1989 .