Bright and dark solitons in the unidirectional long wave limit for the energy transfer on anharmonic crystal lattices

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

“…The oscillation frequency of the HF component against the LF one is found in an integral form. The reported results demonstrate that the solitons found in [21] are stable. The analytical results are confirmed by systematic numerical simulations.…”

“…With an arbitrary value of the 𝛾/𝛽 ratio, the ZS based on Eqs. ( 1) and ( 2) admits an asymptotic solution [21],…”

“…Solitons in such a Zakharov system (ZS) were studied for the following cases: (i) for equal nonlinearity and dispersion coefficients of the LF wave (𝛽 and 𝛾, respectively, see Sec. 2 below) (𝛾/𝛽 = 1), a two-component Davydov-Scott (DS) soliton was found [18,19]; oscillations of the HF component in which were investigated in [20]; (ii) for 𝛾/𝛽 ≠ 1, an asymptotic solution in the form of a multihump soliton, assuming a sufficiently small HF field amplitude in comparison to the LF one, was found in [14]; (iii) a localized steady state of the HF wave field was found, neglecting strictional action of the HF field on LF waves, given that there exists a LF solution in the form of a "depression" soliton [17]; (iv) new two-component solitons with two free parameters were found analytically in [21] in the asymptotic approximation for an arbitrary ratio of nonlinearity 𝛽 and dispersion 𝛾; and, finally, a one-parameter family of exact two-component solitons under the condition of relatively weak dispersion, 𝛾 < 3𝛽, was found in [21].…”

“…In the present work we aim to consider intra-soliton excitations, in the form of oscillations of the HF component about the LF component of the soliton, following work [21]. The study is performed in the framework of the ZS, consisting of a linear-Schrödinger and KdV equations with an arbitrary ratio of 𝛽 and 𝛾 coefficients.…”

Optical–Terahertz Solitons with Tilted Fronts

“…The authors of [30,31] found a soliton-like solution of the Yajima-Oikawa-Korteweg-de Vries system. Its generalization to the case of the dependence of the field on the transverse coordinate yields the solution of the Yajima-Oikawa-Kadomtsev-Petviashvili system of Eqs.…”