Temporal Solitons in Nonlinear Media Modeled by Modified Complex Ginzburg Landau Equation Under Collective Variable Approach

Abstract

In the present paper, we have investigated the possibility of the existence of soliton solution in media modeled by the modified complex Ginzburg Landau equation. We have employed the technique of collective variables (CVs) to obtain a set of six coupled ordinary differential equations, one each for all the CVs included in the ansatz for the pulse. The coupled differential equations for the collective variables have been numerically solved to reveal the pulse dynamics which show stable soliton propagation.

Super-sech soliton dynamics in optical metamaterials using collective variables

“…Optical metamaterials as novel type of microstructured material have been extensively studied [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Metamaterials (MMs) are artificial composite structures with both negative permittivity and negative permeability and fascinating physical properties at terahertz and optical frequencies.…”

“…The transmission of ultrashort pulses through such promising material exhibit unique feature. It is well known that soliton is one of the remarkable nonlinear excitations produced by the balance between nonlinearity and group velocity dispersion [9][10][11][13][14][15][16][17][18][19]. Recent researches point out that ultrashort pulses propagating in MMs can be described by a modified generalized nonlinear Schrödinger equation (GNLSE) in which the linear and nonlinear coefficients can be tailored to attain any combination of signs unachievable in ordinary materials [1][2][3][4][5][6][7][8][9][10][11][12][13].…”

“…The dynamics of soliton propagation through these optical metamaterials is governed by the nonlinear Schrödinger'squation (NLSE) with a few perturbation terms. The integrability aspect of this model was studied with various forms of nonlinearity [9][10][11][12][13][14][15]. Different algorithms are used to yield solitons, shock waves and other solution to the model that appeared with several integrability conditions.…”

Optical Solitons with Power Law Nonlinearity and Hamiltonian Perturbations: An Exact Solution

“…The linearly independent functions in (23) are tanh p+ j τ where j = −2, 0, 2. First, setting the coefficient of tanh p−2 τ to zero yields…”

Optical solitons with log-law nonlinearity

“…The nonlinear Schrd inger's equation (NLSE) plays a very important role in various areas of Physical Sciences [1][2][3][4][5][6][7][8][9][10]. It appears in Nonlinear Optics, Fluid Dynamics, Mathematical Biology, Plasma Physics and many more areas.…”