Soliton oscillations in the Zakharov-type system at arbitrary nonlinearity-dispersion ratio

• Published in: Chaos, solitons and fractals Vol. 117; pp. 264 - 268
• Main Authors: Blyakhman, L.G., Gromov, Е.M., Malomed, B.A., Tyutin, V.V.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01-12-2018
• Subjects: Dispersion; Korteweg-de Vries equation; Linear Schrödinger equation; Nonlinearity; Soliton stability; Two-component solitons; Korteweg-de Vries equation; Soliton stability; Nonlinearity; Two-component solitons; Linear Schrödinger equation; Dispersion
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2018.11.004

•The dynamics of the two-component (HF-LF) soliton with initial displacement of the HF component is investigated.•The study is performed in the framework of the Zakharov-type system of coupled linear-Schrödinger and KdV equations, with an arbitrary ratio of nonlinearity and dispersion coefficients.•Analytical and numerical results are produced.•The oscillation frequency of the displaced HF component of the two-component soliton is found.•Stability of the perturbed two-component solitons is demonstrated.
The dynamics of two-component solitons with a small spatial displacement of the high-frequency (HF) component relative to the low-frequency (LF) one is investigated in the framework of the Zakharov-type system. In this system, the evolution of the HF field is governed by a linear Schrödinger equation with the potential generated by the LF field, while the LF field is governed by a Korteweg-de Vries (KdV) equation with an arbitrary dispersion-nonlinearity ratio and a quadratic term accounting for the HF feedback on the LF field. The oscillation frequency of the soliton's HF component relative to the LF one is found analytically. It is shown that the solitons are stable against small perturbations. The analytical results are confirmed by numerical simulations.