Ref HAL: hal-00266216_v1
DOI: 10.1098/rspa.2007.1861
WoS: 000247906600006
Exporter : BibTex | endNote
18 Citations
Résumé:

The dynamics of a nonlinear and dispersive long surface capillary-gravity wave model equation is studied analytically in its short-wave limit. We exhibit its Lax pair and some non-trivial conserved quantities. Through a change of functions an unexpected connection between this classical surface water wave model and the sine-Gordon (or sinh-Gordon) equation is established. Numerical and analytical studies show that in spite of integrability their solutions can develop singularities and multivaluedness in finite time. These features can be traced to the fact that the surface tension term in the energy involves second-order derivatives. It would be interesting to see in an experiment whether such singularities actually appear, for which surface tension would be specifically responsible.

Ref HAL: in2p3-00149084_v1
Ref Arxiv: hep-th/0703084
DOI: 10.1016/j.nuclphysb.2007.04.018
WoS: 000250291200002
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
31 Citations
Résumé:

A four point function of basic Neveu-Schwarz exponential fields is constructed in the N = 1 supersymmetric Liouville field theory. Although the basic NS structure constants were known previously, we present a new derivation, based on a singular vector decoupling in the NS sector. This allows to stay completely inside the NS sector of the space of states, without referencing to the Ramond fields. The four-point construction involves also the NS blocks, for which we suggest a new recursion representation, the so-called elliptic one. The bootstrap conditions for this four point correlation function are verified numerically for different values of the parameters.

Commentaires: soumis Nuclear Physics B

Ref HAL: hal-00259672_v1
Ref Arxiv: cond-mat/0401324
DOI: 10.1103/PhysRevA.69.053624
WoS: 000221813700139
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
50 Citations
Résumé:

Improving perturbation theory via a variational optimization has generally produced in higher orders an embarrassingly large set of solutions, most of them unphysical (complex). We introduce an extension of the optimized perturbation method which leads to a drastic reduction of the number of acceptable solutions. The properties of this new method are studied and it is then applied to the calculation of relevant quantities in different $\phi^4$ models, such as the anharmonic oscillator energy levels and the critical Bose-Einstein Condensation temperature shift $\Delta T_c$ recently investigated by various authors. Our present estimates of $\Delta T_c$, incorporating the most recently available six and seven loop perturbative information, are in excellent agreement with all the available lattice numerical simulations. This represents a very substantial improvement over previous treatments.

Commentaires: 9 pages

Ref HAL: hal-00266319_v1
Ref Arxiv: physics/0303085
Ref. & Cit.: NASA ADS
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Résumé:

From a columnar approximation of the Euler equations of an incompressible fluid with surface tension, we derive in the short-wave approximation a new integrable classical 1+1 dimensional field theory for the motion of the surface. Together with a Lorentz invariance,this system has the novel feature of solutions which become multiple valued in finite time.

Commentaires: Scattering, Two-Volume Set Scattering and inverse scattering in Pure and Applied Science(Volume 1-2) E. Pike and P.C. Sabatier Eds. Academic Press (2001) pp. 1327-1330. ISBN: 0-12-613760-9

DOI: 10.1088/0266-5611/17/4/317
WoS: 000170573300018
8 Citations
Résumé:

A new nonlinear equation governing asymptotic dynamics of short surface waves is derived by using a short-wave perturbative expansion in an appropriate reduction of the Euler equations. This reduction corresponds to a Green-Naghdi-type equation with a cinematic discontinuity in the surface. The physical system under consideration is an ideal fluid (inviscid, incompressible and without surface tension) in which takes place a steady surface motion. An ideal surface wind on a lake which produces surface flow is a physical environment conducive to the above-mentioned phenomenon. The equation obtained admits peakon solutions with amplitude, velocity and width in interrelation.

Commentaires: SPECIAL ISSUE TO CELEBRATE PIERRE SABATIER'S 65TH BIRTHDAY