Finite time blow-up and breaking of solitary wind waves

The evolution of surface water waves in finite depth under wind forcing is reduced to an antidissipative Korteweg-de Vries-Burgers equation. We exhibit its solitary wave solution. Antidissipation accelerates and increases the amplitude of the solitary wave and leads to blow-up and breaking. Blow-up occurs in finite time for infinitely large asymptotic space so it is a nonlinear, dispersive, and antidissipative equivalent of the linear instability which occurs for infinite time. Due to antidissipation two given arbitrary and adjacent planes of constant phases of the solitary wave acquire different velocities and accelerations inducing breaking. Soliton breaking occurs in finite space in a time prior to the blow-up. We show that the theoretical growth in amplitude and the time of breaking are both testable in an existing experimental facility.

Bright solitons in a quasi-one-dimensional reduced model of a dipolar Bose-Einstein condensate with repulsive short-range interactions

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

N=1 super sinh-Gordon model in the half line: breather solutions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Wide vector solitons in systems with time- and space-modulated nonlinearities

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On the mKdV-Liouville hierarchy and its self-similarity reduction

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Stable and mobile excited two-dimensional dipolar Bose-Einstein condensate solitons

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Equação de Schrödinger não linear com coeficientes modulados

Pós-graduação em Física - FEG

Toroidal solitons in 3+1 dimensional integrable theories

We analyze the integrability properties of models defined on the symmetric space SU(2)/U(1) in 3 + 1 dimensions, using a recently proposed approach for integrable theories in any dimension. We point out the key ingredients for a theory to possess an infinite number of local conservation laws, and discuss classes of models with such property, We propose a 3 + 1-dimensional, relativistic invariant field theory possessing a toroidal soliton solution carrying a unit of topological charge given by the Hopf map. Construction of the action is guided by the requirement that the energy of static configuration should be scale invariant. The solution is constructed exactly. The model possesses an infinite number of local conserved currents. The method is also applied to the Skyrme-Faddeev model, and integrable submodels are proposed. (C) 1999 Elsevier B.V. B.V. All rights reserved.

Hirota's solitons in the affine and the conformal affine Toda models

We use Hirota's method formulated as a recursive scheme to construct a complete set of soliton solutions for the affine Toda field theory based on an arbitrary Lie algebra. Our solutions include a new class of solitons connected with two different types of degeneracies encountered in Hirota's perturbation approach. We also derive an universal mass formula for all Hirota's solutions to the affine Toda model valid for all underlying Lie groups. Embedding of the affine Toda model in the conformal affine Toda model plays a crucial role in this analysis.

Simetrias e sólitons do modelo de toda conforme afim

Pós-graduação em Física - IFT

Estrutura algébrica dos modelos integráveis

Pós-graduação em Física - IFT