Deformations of KdV and soliton collisions

Blas, H.; Ochoa, R.; Suárez, Diego Berdeja

doi:10.1088/1742-6596/1558/1/012012

Cited by 3 publications

(27 citation statements)

References 14 publications

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“…In the context of deformed sine-Gordon and KdV models there have been analyzed the behavior of novel infinite towers of asymptotically conserved (anomalous) charges in [14] and [15], respectively. Those results uncovered new anomalous charges and extended the earlier results on SG model in [4,5,9] and KdV model in [10], respectively.…”

Section: Modified Nls and Anomalous Chargesmentioning

confidence: 99%

“…Remarkably, it has been observed that even the standard KdV model possesses several towers of quasiconservation laws with anomalous charges for analytical N − soliton configurations satisfying the special P s T d symmetry properties [15]. For the standard SG theory this property has also been discussed for the 2-soliton sector of the theory [14].…”

Section: Introductionmentioning

confidence: 97%

“…Recently, some deformations of integrable models, which exhibit soliton-type properties, have been put forward. Various quasi-integrability properties of the deformations of the integrable models, such as SG, NLS, Toda, KdV, Boullogh-Dodd and SUSY-SG have recently been examined in the frameworks of the anomalous zero-curvature formulations [4,5,6,7,8,9,10,11,12,13] and the deformations of the Riccati-type pseudo-potential approach [14,15].…”

Section: Introductionmentioning

confidence: 99%

“…Fourth, the existence of several towers of infinitely many anomalous charges. Several new towers of anomalous charges have been uncovered in [14,15], in this way adding a new list to the ones presented in [4,9,11,12] for deformations of SG and KdV models. Fifth, some deformed models possess a subset of infinite number of anomalous charges for soliton eigenstates simply of the shifted space-reflection symmetry P s .…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, in the context of the Riccati-type pseudo-potential approach to quasi-integrability, there have been shown that the deformed SG and KdV models [14,15] can be formulated as the compatibility condition of certain linear systems of equations and that they possess infinite towers of exact non-local conservation laws.…”

Section: Introductionmentioning

confidence: 99%

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Modified non-linear Schrödinger models, ${\cal C}{\cal P}_s{\cal T}_d$ invariant $N-$bright solitons and infinite towers of anomalous charges

Blas,

Maguiña,

Santos

2020

Preprint

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Modifications of the non-linear Schrödinger model (MNLS) i∂tψ(x, t) + ∂ 2x ψ(x, t) − [ δV δ|ψ| 2 ]ψ(x, t) = 0, where ψ ∈ C and V : IR+ → IR, are considered. We show that the quasi-integrable MNLS models possess infinite towers of quasi-conservation laws for soliton-type configurations with a special complex conjugation, shifted parity and delayed time reversion (CPsT d ) symmetry. Infinite towers of anomalous charges appear even in the standard NLS model for CPsT d invariant N −bright solitons. The true conserved charges emerge through some kind of anomaly cancellation mechanism, since a convenient linear combination of the relevant anomalies vanish. A Riccati-type pseudo-potential is introduced for a modified AKNS system (MAKNS), which reproduces the MNLS quantities upon a reduction process. Two infinite towers of exact non-local conservation laws are uncovered in this framework. Our analytical results are supported by numerical simulations of 2−bright-soliton scatterings with potentialOur numerical simulations show the elastic scattering of bright solitons for a wide range of values of the set {η, ǫ} and a variety of amplitudes and relative velocities. The AKNS-type system is quite ubiquitous, and so, our results may find potential applications in several areas of non-linear physics, such as Bose-Einstein condensation, superconductivity, soliton turbulence and the triality among gauge theories, integrable models and gravity theories.

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Section: Modified Nls and Anomalous Chargesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Modified non-linear Schrödinger models, ${\cal C}{\cal P}_s{\cal T}_d$ invariant $N-$bright solitons and infinite towers of anomalous charges

Blas,

Maguiña,

Santos

2020

Preprint

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Modified AKNS model, Riccati-type pseudo-potential approach and infinite towers of quasi-conservation laws

Blas,

Maguiña,

Santos

2022

Preprint

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A dual Riccati-type pseudo-potential formulation is introduced for a modified AKNS system (MAKNS) and infinite towers of novel anomalous conservation laws are uncovered. In addition, infinite towers of exact non-local conservation laws are uncovered in a linear formulation of the system. It is shown that certain modifications of the non-linear Schrödinger model (MNLS) can be obtained through a reduction process starting from the MAKNS model. So, the novel infinite sets of quasi-conservation laws and related anomalous charges are constructed by an unified and rigorous approach based on the Riccati-type pseudo-potential method, for the standard NLS and modified MNLS cases, respectively. The non-local properties, the complete list of towers of infinite number of anomalous charges and the (non-local) exact conservation laws of the quasi-integrable systems, such as the deformed Bullough-Dodd, Toda, KdV and SUSY sine-Gordon systems can be studied in the framework presented in this paper. Our results may find many applications since the AKNS-type system arises in several branches of non-linear physics, such as Bose-Einstein condensation, superconductivity and soliton turbulence.

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Majorana zero mode-soliton duality and in-gap and BIC bound states in modified Toda model coupled to fermion

Blas,

Monsalve,

Quicaño

et al. 2022

Preprint

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A two-dimensional field theory of a fermion chirally coupled to Toda field plus a scalar self-coupling potential is considered. Using techniques of integrable systems we obtain analytical zero modes, in-gap states and bound states in the continuum (BIC) for topological configurations of the scalar field. Fermionsoliton duality mappings are uncovered for the bound state spectrum, which interpolates the weak and strong coupling sectors of the model and give rise to novel Thirring-like and multi-frequency sine-Gordon models, respectively. The non-perturbative effects of the back-reaction of the fermion bound states on the kink are studied and it is shown that the zero mode would catalyze the emergence of a new kink with lower topological charge and greater slope at the center, in the strong coupling limit of the model. For special topological charges and certain relative phases of the fermion components it is shown that the kinks can host Majorana zero modes. Our results may find applications in several branches of non-linear physics, such as confinement in QCD 2 , braneworld models, high T c superconductivity and topological quantum computation. We back up our results with numerical simulations for continuous families of topological sectors.

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Deformations of KdV and soliton collisions

Cited by 3 publications

References 14 publications

Modified non-linear Schrödinger models, ${\cal C}{\cal P}_s{\cal T}_d$ invariant $N-$bright solitons and infinite towers of anomalous charges

Modified non-linear Schrödinger models, ${\cal C}{\cal P}_s{\cal T}_d$ invariant $N-$bright solitons and infinite towers of anomalous charges

Modified AKNS model, Riccati-type pseudo-potential approach and infinite towers of quasi-conservation laws

Majorana zero mode-soliton duality and in-gap and BIC bound states in modified Toda model coupled to fermion

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