Optical solitons and complexitons of the Schrödinger–Hirota equation

Dispersive optical solitons by Kudryashov's method

“…Let us demonstrate the application of Kudryashov method for finding the new exact traveling wave solutions of SHE with power law nonlinearity [25] in the following form…”

“…SHE is obtained from NLSE with Kerr law nonlinearity and third order dispersion (3OD) by the aid of Lie symmetry analysis, with a valid approximation. The details are obtained earlier [25,29,30]. Both NLSE and SHE are nonlinear partial differential equations of S-type.…”

“…Both NLSE and SHE are nonlinear partial differential equations of S-type. SHE was studied earlier on several occasions [25,[28][29][30]. The exact 1-soliton solutions were obtained.…”

Gaussian-type light bullets in power-law nonlinear media withPT-symmetricpotentials

“…In the last few decades, the dynamical propagation of solitons as the ultra-short and strong laser pulses was intensively investigated [7][8][9]. Spatiotemporal solitons [also called "light bullets" (LBs)] [10][11][12] exist due to the result of the simultaneous balance of diffraction and group velocity dispersion (GVD) by the transverse self-focusing and nonlinear phase modulation in the longitudinal direction, respectively.…”

Modified Simple Equation Method and its Applications to Nonlinear Partial Differential Equations

“…Searching for exact soliton solutions of NPDEs has been played significant role in the study of dynamics of observed phenomena [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19]. Many new methods for obtaining exact solutions to NPDEs have been proposed.…”