A new conserved quantity for non-Kerr law optical solitons

Soliton Parameter Dynamics in a Non-Kerr Law Media

“…Equation (1) has three integrals of motion [5] also known as the conserved quantities. They are the energy (E) also known as the wave power or L 2 norm, linear momentum (M ) and the Hamiltonian (H) that are respectively given by…”

“…Besides these conserved quantities, the conserved quantity that governs the conservation of phase is given by [5,17] …”

“…This conservation law provides the law of variation of the soliton phase θ that is defined in (4). For the soliton given by (3), the parameters are now defined as follows [5] …”

“…In (31), δ is the coefficient of nonlinear damping or amplification [5] depending on its sign and m could be 0, 1, 2. For m = 0, δ is the linear amplification or attenuation according to δ being positive or negative.…”

“…The origin of nonlinear response is related to the nonharmonic motion of bound electrons under the influence of an applied field. As a result the Fourier amplitude of the induced polarization from the electric dipoles is not linear in the electric field, but involves higher terms in electric field amplitude [1][2][3][4][5][6][7][8][9][10][11]. For Kerr law, F (s) = s. Thus, the NLSE modifies to…”