A study of optical solitons with Kerr and power law nonlinearities by He’s variational principle

Abstract

This paper studies optical solitons, in presence of perturbation terms, by the aid of He's variational principle. The intermodal dispersion, self-steepening and nonlinear dispersion are all treated as perturbation terms. Both Kerr law as well as power law nonlinearities are considered in this paper.

Optical Solitons With Higher Order Dispersion by Semi-Inverse Variational Principle

“…Here, in (18), the parameters A and B represent the amplitude and inverse width of the soliton respectively, and the functional f depends on whether the nonlinear function F is Kerr or power. HVP states that the parameters A and B are determined from the solution of the equations [17,32,35]…”

“…The origin of nonlinear response is related to the non-harmonic motion of bound electrons under the influence of an applied field. As a result the induced polarization is not linear in the electric field, but involves higher order terms in electric field amplitude [16,17,35,36].…”

“…It needs to be noted that this principle was already applied to study optical solitons with Raman scattering, self-steepening, nonlinear dispersion as well as intermodal dispersion terms [17,35]. Subsequently, this principle was applied to study the same perturbation terms but with full nonlinearity, where the nonlinear terms are generalized to an arbitrary exponent [35].…”

“…Subsequently, this principle was applied to study the same perturbation terms but with full nonlinearity, where the nonlinear terms are generalized to an arbitrary exponent [35]. In this paper, HVP will be used to study optical soliton perturbation with higher order dispersion terms.…”

Optical Soliton Perturbation With Log Law Nonlinearity by He's Semi-Inverse Variational Principle

“…[1][2][3][4][5][6][7][8][9][10] In fact optical solitons are now out of the lab stage and is a reality in many continents. Optical solitons now do propagate over transcontinental and transoceanic distances through underwater optical fibers.…”