Riccati-type pseudopotentials, conservation laws and solitons of deformed sine-Gordon models

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

“…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.…”

“…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]. So, one can argue that the truly integrable systems inherit certain properties to their deformed counterparts.…”

“…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].…”

“…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 .…”

“…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.…”