TY - JOUR

T1 - Bi-Solitons on the Surface of a Deep Fluid: An Inverse Scattering Transform Perspective Based on Perturbation Theory

AU - Gelash, Andrey

AU - Dremov, Sergey

AU - Mullyadzhanov, Rustam

AU - Kachulin, Dmitry

N1 - The work of A. G. was funded by the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 101033047. The work of S. D. and D. K. on obtaining and studying bi-solitons in the deep fluid models was supported by the RSF Grant No. 19-72-30028-II. The work of R. M. on IST perturbation theory analysis was supported by RSF Grant No. 19-79-30075-II.

PY - 2024/3/29

Y1 - 2024/3/29

N2 - We investigate theoretically and numerically the dynamics of long-living oscillating coherent structures - bi-solitons - in the exact and approximate models for waves on the free surface of deep water. We generate numerically the bi-solitons of the approximate Dyachenko-Zakharov equation and fully nonlinear equations propagating without significant loss of energy for hundreds of the structure oscillation periods, which is hundreds of thousands of characteristic periods of the surface waves. To elucidate the long-living bi-soliton complex nature we apply an analytical-numerical approach based on the perturbation theory and the inverse scattering transform (IST) for the one-dimensional focusing nonlinear Schrödinger equation model. We observe a periodic energy and momentum exchange between solitons and continuous spectrum radiation resulting in repetitive oscillations of the coherent structure. We find that soliton eigenvalues oscillate on stable trajectories experiencing a slight drift on a scale of hundreds of the structure oscillation periods so that the eigenvalue dynamics is in good agreement with predictions of the IST perturbation theory. Based on the obtained results, we conclude that the IST perturbation theory justifies the existence of the long-living bi-solitons on the surface of deep water that emerge as a result of a balance between their dominant solitonic part and a portion of continuous spectrum radiation.

AB - We investigate theoretically and numerically the dynamics of long-living oscillating coherent structures - bi-solitons - in the exact and approximate models for waves on the free surface of deep water. We generate numerically the bi-solitons of the approximate Dyachenko-Zakharov equation and fully nonlinear equations propagating without significant loss of energy for hundreds of the structure oscillation periods, which is hundreds of thousands of characteristic periods of the surface waves. To elucidate the long-living bi-soliton complex nature we apply an analytical-numerical approach based on the perturbation theory and the inverse scattering transform (IST) for the one-dimensional focusing nonlinear Schrödinger equation model. We observe a periodic energy and momentum exchange between solitons and continuous spectrum radiation resulting in repetitive oscillations of the coherent structure. We find that soliton eigenvalues oscillate on stable trajectories experiencing a slight drift on a scale of hundreds of the structure oscillation periods so that the eigenvalue dynamics is in good agreement with predictions of the IST perturbation theory. Based on the obtained results, we conclude that the IST perturbation theory justifies the existence of the long-living bi-solitons on the surface of deep water that emerge as a result of a balance between their dominant solitonic part and a portion of continuous spectrum radiation.

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85188892790&origin=inward&txGid=8824a8d899039ccec6b4e5f63f82da18

UR - https://www.mendeley.com/catalogue/4fe6b66c-b65c-3189-a612-7301d9e13af1/

U2 - 10.1103/PhysRevLett.132.133403

DO - 10.1103/PhysRevLett.132.133403

M3 - Article

C2 - 38613282

VL - 132

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 13

M1 - 133403

ER -