Diffusion of overdamped classical solitons

We study the diffusion and deformation of classical solitons coupled to thermal noise. The diffusion coefficient for kinds in the gf⁴ theory is predicted up to the second order in kT. The prediction is verified by numerical simulations. Multiskyrmions in the vector O(3) sigma model are studied within the same formalism. Thermal noise results in a diffusion on the multisoliton collective coordinate space (moduli space). There are entropic forces which tend, for example, to bind pairs of solitons into bi-solitonic molecules.     

Interaction of two-space-dimensional classical Q solitons

The stability region and the head-on collisions of two-space-dimensional “charged” (x, y, t) solitons have been investigated via a computer in the framework of the Lorentz-invariant Klein-Gordon equation with saturable nonlinearity. The range of parameters has been determined where (i) quasi-elastic soliton interaction occurs and (ii) the formation of two soliton bound states takes place. The collision of solitons may lead to their decay.     

Excitation of low-amplitude solitons in systems with decay instability

A nonlinear equation for the interaction of a pair of opposite-traveling waves with a normally incident decay mode has been derived. It is shown that solutions of the equation are low-amplitude solitons of a new type.     

Symmetry-breaking instability of multimode vector solitons

We show experimentally that the two-component multimode spatial optical vector soliton, i.e., a two-hump self-guided laser beam, exhibits in Kerr media a sharp space-inversion symmetry-breaking instability. The experiment is performed in a CS2 planar waveguide using the orthogonal circular polarization states of light as the two components of the vector soliton.     

Snake instability of one-dimensional parametric spatial solitons

We show that one-dimensional parametric spatial solitons undergo temporal instability that leads to their breakup into spatiotemporal patterns with a characteristic snakelike shape.     

Condition for convective instability of dark solitons

Simple derivation of the condition for the transition point from absolute instability of plane dark solitons to their convective instability is suggested. It is shown that unstable wave packet expands with velocity equal to the minimal group velocity of the disturbance waves propagating along a dark soliton. The growth rate of the length of dark solitons generated by the flow of Bose-Einstein condensate past an obstacle is estimated. Analytical theory is confirmed by the results of numerical simulations.     

Modulational instability and complex dynamics of confined matter-wave solitons

We study the formation of bright solitons in a Bose-Einstein condensate of 7Li atoms induced by a sudden change in the sign of the scattering length from positive to negative, as reported in a recent experiment [Nature (London) 417, 150 (2002)]]. The numerical simulations are performed by using the Gross-Pitaevskii equation with a dissipative three-body term. We show that a number of bright solitons is produced and this can be interpreted in terms of the modulational instability of the time-dependent macroscopic wave function of the Bose condensate. In particular, we derive a simple formula for the number of solitons that is in good agreement with the numerical results. We find that during the motion of the soliton train in an axial harmonic potential the number of solitonic peaks changes in time and the density of individual peaks shows an intermittent behavior.     

Transverse instability of optical spatiotemporal solitons in quadratic media

We present experimental and numerical observations of transverse instability in quadratic media under conditions that emphasize the inherently spatiotemporal and multidimensional nature of the wave propagation. Intensity-dependent beam filamentation is shown to be closely connected to the periodic evolution of quadratic solitons, and implications for the generation of three-dimensional spatiotemporal solitons are discussed.     

Transverse instability of strongly coupled dark-bright Manakov vector solitons

We show, by performing linear stability analysis and direct numerical simulations, that dark-soliton transverse instability is significantly reduced in Kerr media by strong coupling to a bright soliton. High instability suppression can be achieved by use of large-amplitude bright solitons.     

Effective dynamics of a classical point charge

The effective Lagrangian of a point charge is derived by eliminating the electromagnetic field within the framework of the classical closed time path formalism. The short distance singularity of the electromagnetic field is regulated by an UV cutoff. The Abraham–Lorentz force is recovered and its similarity to quantum anomalies is underlined. The full cutoff-dependent linearized equation of motion is obtained, no runaway trajectories are found but the effective dynamics shows acausality if the cutoff is beyond the classical charge radius. The strength of the radiation reaction force displays a pole in its cutoff-dependence in a manner reminiscent of the Landau-pole of perturbative QED. Similarity between the dynamical breakdown of the time reversal invariance and dynamical symmetry breaking is pointed out.     

Transverse instability of vector solitons and generation of dipole arrays

We develop a theory of modulational instability of multiparameter solitary waves and analyze the transverse instability of composite (or vector) optical solitons in a saturable nonlinear medium. We demonstrate theoretically and experimentally that a soliton stripe breaks up into an array of ( 2+1)-dimensional dipole-mode vector solitons, thus confirming the robust nature of those solitons as fundamental composite structures of incoherently coupled fields.     

Modulational instability of dark solitons in three wave resonant interaction

We study the propagation of velocity-locked dark triplet solitons in the three wave resonant interaction model. The modulational instability of the plane wave background where the solitons sit prevents the long range propagation. However even a small second order dispersion proves to greatly reduce, or suppress, the modulational instability gain, allowing for effective stable soliton propagation.     

Elimination of transverse instability in stripe solitons by one-dimensional lattices

We demonstrate theoretically and experimentally that the transverse instability of coherent soliton stripes can be greatly suppressed or totally eliminated when the soliton stripes propagate in a one-dimensional photonic lattice under self-defocusing nonlinearity.     

水波孤子起始不稳定性的实验研究

系统地测量了小宽度的矩型水槽中的自调制(0,1)模孤波起始不稳定性与液体深度、水槽宽度、混合液体中甘油体积比等因素之间的关系。实验发现液体深度、容器宽度的减小及混合液体中甘油体积比的增加都会导致起始激励加速度的变大并引起一定的频移。实验结果与理论计算达到了令人满意的定性相似。