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most citedCorrelation functions of the open XXZ chain I

109 citations

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math.AP2009★ 1 cited

Transverse instability of the line solitary water-waves

Frederic Rousset, Nikolay Tzvetkov

We prove the linear and nonlinear instability of the water line solitary waves with respect to transverse perturbations.

math.AP2008

The cubic fourth-order Schrodinger equation

Benoit Pausader

We investigate the cubic defocusing fourth order Schrödinger equation in arbitrary space dimension for arbitrary initial data. We prov…

math.AP2007★ 12 cited

Scattering for H^1/2 bounded solutions to the cubic, defocusing NLS in 3 dimensions

Carlos E. Kenig, Frank Merle

We show that if a solution of the defocusing cubic NLS in 3d remains bounded in the homogeneous Sobolev norm of order 1/2 in its maximal interval of existence, then the interval is…

math.AP2007

Dynamic of threshold solutions for energy-critical NLS

Thomas Duyckaerts, Frank Merle

We consider the radial energy-critical non-linear focusing Schrödinger equation in dimension N=3,4,5. An explicit stationnary solution, W, of this equation is known. In a previous…

math.AP2007★ 3 cited

Asymptotic stability of solitons of the gKdV equations with general nonlinearity

Yvan Martel, Frank Merle

We consider the generalized Korteweg-de Vries equation \partial_t u + \partial_x (\partial_x^2 u + f(u))=0, \quad (t,x)\in [0,T)\times \mathbb{R}, (1) with general nonlineari…

math.AP2002

Fourth order equations of critical Sobolev growth. Energy function and solutions of bounded energy in the conformally flat case

Veronica Felli, Emmanuel Hebey, Frederic Robert

In this paper we study the energy function associated to fourth order equations of critical growth on smooth compact conformally flat manifolds of dimension greater or equal than 5…