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Article overview
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Quasi-integrable KdV models, towers of infinite number of anomalous charges and soliton collisions | H. Blas
; R. Ochoa
; D. Suarez
; | Date: |
8 Jan 2020 | Abstract: | We found, through analytical and numerical methods, new towers of infinite
number of asymptotically conserved charges for deformations of the Korteweg-de
Vries equation (KdV). It is shown analytically that the standard KdV also
exhibits some towers of infinite number of anomalous charges, and that their
relevant anomalies vanish for $N-$soliton solution. Some deformations of the
KdV model are performed through the Riccati-type pseudo-potential approach, and
infinite number of exact non-local conservation laws is provided using a linear
formulation of the deformed model. In order to check the degrees of
modifications of the charges around the soliton interaction regions, we compute
numerically some representative anomalies, associated to the lowest order
quasi-conservation laws, depending on the deformation parameters ${epsilon_1,
epsilon_2}$, which include the standard KdV ($epsilon_1=epsilon_2=0$), the
regularized long-wave (RLW) ($epsilon_1=1,epsilon_2=0$), the modified
regularized long-wave (mRLW) ($epsilon_1=epsilon_2=1$) and the KdV-RLW
(KdV-BBM) type ($epsilon_2=0,,epsilon
eq {0,1}$) equations,
respectively. Our numerical simulations show the elastic scattering of two and
three solitons for a wide range of values of the set ${epsilon_1,
epsilon_2}$, for a variety of amplitudes and relative velocities. The
KdV-type equations are quite ubiquitous in several areas of non-linear science,
and they find relevant applications in the study of General Relativity on
$AdS_{3}$, Bose-Einstein condensates, superconductivity and soliton gas and
turbulence in fluid dynamics. | Source: | arXiv, 2001.2471 | Services: | Forum | Review | PDF | Favorites |
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