Optical Solitons in Photonic Nano Waveguides with an Improved Nonlinear Schrödinger's Equation

[INVITED] Soliton propagation through nanoscale waveguides in optical metamaterials

“…From (22) and (28) (7), (36) and (37) with (42). Therefore, dark 1-soliton solution for power law nonlinearity is also given by (14) with the wave number as in (16) and the relation between the free parameters as in (15). The constraint (13) also remains valid, in this case.…”

Singular optical solitons in birefringent nano-fibers

“…The ansatz method is used. In order to set up the starting point, the solitons are written in the phase-amplitude format as [1,16,17] ( )…”

“…In order to seek singular soliton solutions of second type, for birefringent fibers with parabolic law, the starting hypothesis is taken to be [16,17,19,20]:…”

Analytic study on the generalized ( $$3+1$$ 3 + 1 )-dimensional nonlinear Schrödinger equation with variable coefficients in the inhomogeneous optical fiber

“…Theoretical contributions to the development of the soliton theory have been made [4][5][6]. Due to the potential of optical solitons in the optical fiber transmission systems [7][8][9][10][11][12][13][14][15][16][17], attention has been paid to the NLS-type equations [18][19][20][21][22]. In order to study the NLS-type equations, methods have been proposed, such as the inverse scattering transformation [23], Bäcklund transformation [24][25][26] and Darboux transformation [27,28].…”