Soliton Parameter Dynamics in a Non-Kerr Law Media

Abstract

Abstract-The adiabatic parameter dynamics of non-Kerr law optical solitons is obtained in this paper by the aid of soliton perturbation theory. The various kinds of perturbation terms that arise exhaustively in the context of optical solitons are considered in this paper. The new conserved quantity is also used to obtain the adiabatic dynamics of the soliton phase in all cases of non-Kerr laws studied in this paper. The non-Kerr law nonlinearities that are considered in this paper are power law, parabolic law as well as the dual-power law.

Topological 1-soliton solution of the Biswas–Milovic equation with power law nonlinearity

“…This pair of equations will now be further analyzed for obtaining the exact 1-soliton solution to (6). This is done in Section 3.1.…”

“…(6) will now be integrated by the soliton ansatz method. In this paper, the focus is going to be on obtaining the topological soliton solution to (6). In order to solve (6), the starting hypothesis will stay the same as in (2), where the phase of the soliton is given by [1,2,13,14] φ(x, t) = −κ(t)x + ω(t)t + θ (t).…”

“…The study of the integrability aspects of nonlinear evolution equations has been going on for the past few decades [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. There are various techniques that have been developed during this time frame to carry out the integration of these equations.…”

Evolution and Collapse of a Lorentz Beam in Kerr Medium

“…The Kerr medium has an intensity-dependent refractive index, n = n 0 + n 2 |E| 2 that is due to third order nonlinear response of the polarization to electric field of the beam or laser light. Recent works have studied the propagation of elliptic Gaussian beam [11] and beams with unequal transverse widths [12] in Kerr medium, as well as soliton propagation in Kerr [13] and non-Kerr law media [14]. We compute the spatial distribution of the Lorentz beam as it propagates through the nonlinear Kerr medium, including the critical power and collapse.…”

Nonlinear Dynamics of FPU Lattice Type Protein Molecular Chain

“…Davydov [1] considered a mathematical model to study the energy transfer in alpha-helical proteins, and he showed that the transport of the hydrolysis energy of ATP along alpha-helical proteins is through the formation of solitons moving without loss of energy [2][3][4][5]. In all the works [6][7][8][9][10][11][12] that followed Davydov, the dynamics is studied by proposing suitable Hamiltonian including interactions of different types such as molecular excitations, dipole-dipole interactions, vibrational excitations, coupling between exciton and phonon, quadrupole-quadrupole type interactions, interspine coupling etc. The dynamics associated with the above models is found to be governed by nonlinear Schrӧdinger type equations.…”