Controllability for two-Kuznetsov-Ma solitons in a (2 + 1)-dimensional graded-index grating waveguide

Nonlinear tunnelling effect of combined Kuznetsov–Ma soliton in (3+1)-dimensional $${{\varvec{\mathcal {PT}}}}$$ PT -symmetric inhomogeneous nonlinear couplers with gain and loss

“…Many authors [46,47] have discussed the controllable behaviors of KM soliton based on the concept of nonautonomous solitons [48]. In this present paper, we focus on the (3+1)-dimensional CNLSE in the inhomogeneous PTsymmetric nonlinear couplers and its combined KM soliton solution.…”

Sequential excitations of Peregrine solution structures in combined Ma breathers for a (3+1)-dimensional coupled partially nonlocal nonlinear Schrödinger equation

“…The combined Ma breather was firstly constructed for the (1+1)-dimensional NLSE [27]. After that, higher dimensional Ma breathers were studied [28][29][30]. The controllability for two Ma breathers in a (2+1)-dimensional graded-index grating waveguide was discussed [28].…”

“…After that, higher dimensional Ma breathers were studied [28][29][30]. The controllability for two Ma breathers in a (2+1)-dimensional graded-index grating waveguide was discussed [28]. A controllable combined Peregrine soliton and Ma breather in PTsymmetric nonlinear couplers with gain and loss was also studied [29].…”

“…Moreover, vector combined and crossing Mabreathers in PT-symmetric coupled waveguides were investigated [30]. However, these higher dimensional Ma breathers discussed in [28][29][30] are not actually localized in space coordinates. In this paper, we focus on the spatially localized Ma breathers, and study the sequential excitation of PS structures in combined Ma breathers based on the following (3+1)-dimensional coupled partially nonlocal PN-NLSE [31].…”

Periodic modulations controlling Kuznetsov–Ma soliton formation in nonlinear Schrödinger equations

“…The appearance of a novel multiple compression point structure in a periodically modulated NLSE, referred to as a Peregrine comb, has been reported recently [24]. The controllable behavior, including partial excitation, maintenance, and postponement of the Peregrine, the AB and KM solitons have also been discussed in certain variable coefficient NLSE [25,26] describing dispersion decreasing fibers. Additionally, the modulational instability of the KM soliton in optical fibers with periodic dispersion was investigated in [27].…”