RETRACTED: An analytical approach to soliton of the saturable non-linear Schrödinger equation determination and consideration of stability of solitary solutions of cubic–quintic non-linear Schrödinger equation (CQNLSE)

Ultrashort self-similar solutions of the cubic-quintic nonlinear Schrödinger equation with distributed coefficients in the inhomogeneous fiber

“…Another interesting self-similar periodic wave and its corresponding localized wave for the CQNLSE (1) are found for expression (17). Figure 7 displays this chirped self-similar periodic wave.…”

“…To illustrate our results (15) and (17), let us pay attention to the compression problem of the laser pulse in an exponential DDF with the dispersion and nonlinearity parameter [20] according to β(z) = β 0 exp(β 1 z), χ(z) = χ 0 exp(χ 1 z), and a small constant gain/loss parameter γ (z) = γ 0 . In this system, χ 0 and χ 1 are the parameters describing Kerr nonlinearity, and the parameters β 0 and β 1 (β 1 < 0 for the DDF) control the rate of dispersion change inside the fiber.…”

“…Senthilnathan et al [15] found the chirped bright soliton solutions in the anomalous and normal dispersion regimes. The variational approach [16] and the analytical approach [17] have been developed for the CQNLSE. Recently, Avelar et al and Belmonte-Beitia et al [18] obtained periodic wave and soliton solutions with cubic and quintic nonlinearities modulated in space and time.…”

Switching behavior of a nonlinear Mach–Zehnder interferometer: Saturating nonlinearity

“…n (x,z) is expressed as [11] nðx,zÞ ¼ n L ðx,zÞ ð for LAÞ n NL ðx,zÞþDnðx,zÞ ðfor NLAÞ Dn(x,z) is its intensity dependent refractive index change which is expressed as [16] Dnðx,zÞ %…”

Optical solitons in a power law media with fourth order dispersion

“…The governing equation in the nonlinear Schrödinger's equation (NLSE) [1][2][3][4][5][6][7][8][9][10]. In general, this equation is studied with various forms of nonlinearity [5] besides the well known Kerr law nonlinearity.…”