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The concept of quasiintegrability for modified nonlinear Schrödinger models
 Journal of High Energy Physics, JHEP
"... We consider modifications of the nonlinear Schrödinger model (NLS) to look at the recently introduced concept of quasiintegrability. We show that such models possess an infinite number of quasiconserved charges which present intriguing properties in relation to very specific spacetime parity tr ..."
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We consider modifications of the nonlinear Schrödinger model (NLS) to look at the recently introduced concept of quasiintegrability. We show that such models possess an infinite number of quasiconserved charges which present intriguing properties in relation to very specific spacetime parity transformations. For the case of twosoliton solutions where the fields are eigenstates of this parity, those charges are asymptotically conserved in the scattering process of the solitons. Even though the charges vary in time their values in the far past and the far future are the same. Such results are obtained through analytical and numerical methods, and employ adaptations of algebraic techniques used in integrable field theories. Our findings may have important consequences on the applications of these models in several areas of nonlinear science. We make a detailed numerical study of the modified NLS potential of the form V ∼ (  ψ 2)2+ε, with ε being a perturbation parameter. We perform numerical simulations of the scattering of solitons for this model and find a good agreement with the results predicted by the analytical considerations. Our paper shows that the quasiintegrability concepts recently proposed in the context of modifications of the sineGordon model remain valid for perturbations of the NLS model. ar
W.J.Zakrzewski: “Numerical and analytical tests of quasiintegrability in modified sineGordon models
 J. High Energy Phys
, 2014
"... Following our attempts to define quasiintegrability in which we related this concept to a particular symmetry of the twosoliton function we check this condition in three classes of modified SineGordon models in (1+1) dimensions. We find that the numerical results seen in various scatterings of tw ..."
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Following our attempts to define quasiintegrability in which we related this concept to a particular symmetry of the twosoliton function we check this condition in three classes of modified SineGordon models in (1+1) dimensions. We find that the numerical results seen in various scatterings of two solitons and in the time evolution of breatherlike structures support our ideas about the symmetry of the field configurations and its effects on the anomalies of the conservation laws of the charges.ar X iv
The concept of quasiintegrability
"... Abstract. We show that certain field theory models, although nonintegrable according to the usual definition of integrability, share some of the features of integrable theories for certain configurations. Here we discuss our attempt to define a “quasiintegrable theory”, through a concrete example: ..."
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Abstract. We show that certain field theory models, although nonintegrable according to the usual definition of integrability, share some of the features of integrable theories for certain configurations. Here we discuss our attempt to define a “quasiintegrable theory”, through a concrete example: a deformation of the (integrable) sineGordon potential. The techniques used to describe and define this concept are both analytical and numerical. The zerocurvature representation and the abelianisation procedure commonly used in integrable field theories are adapted to this new case and we show that they produce asymptotically conserved charges that can then be observed in the simulations of scattering of solitons.
Breatherlike structures in modified sineGordon models
"... We report analytical and numerical results on breatherlike field configurations in a theory which is a deformation of the integrable sineGordon model in (1+1) dimensions. The main motivation of our study is to test the ideas behind the recently proposed concept of quasiintegrability, which emerg ..."
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We report analytical and numerical results on breatherlike field configurations in a theory which is a deformation of the integrable sineGordon model in (1+1) dimensions. The main motivation of our study is to test the ideas behind the recently proposed concept of quasiintegrability, which emerged from the observation that some field theories present an infinite number of quantities which are asymptotically conserved in the scattering of solitons, and periodic in time in the case of breatherlike configurations. Even though the mechanism responsible for such phenomena is not well understood yet, it is clear that special properties of the solutions under a spacetime parity transformation play a crucial role. The numerical results of the present paper give support for the ideas on quasiintegrability, and it is found that extremely longlived breather configurations satisfy these parity properties. We also report on a mechanism, particular to the theory studied here, that favours the existence of long lived breathers even in cases of significant deformations of the sineGordon potential. ar