Abstract
By means of the variational formalism for the nonlinear Schrodinger equation, we find an explicit relation for the power of a pulse in terms of its duration, chirp and fiber parameters (group-velocity dispersion and self-phase modulation parameters). Then, using that relation, we derive the explicit analytical expressions for the variational equations corresponding to the amplitude, width, and chirp of the pulse. The derivation of the analytical expressions for the variational equations is possible for the condition when the Hamiltonian of the system is zero. Finally, for Gaussian and hyperbolic secant ansatz, we show good agreement between the results obtained from the analytical expressions and the direct numerical simulation of the nonlinear Schrodinger equation.
| Original language | English |
|---|---|
| Article number | 026603 |
| Number of pages | 4 |
| Journal | Physical Review. E, Statistical, Nonlinear and Soft Matter Physics |
| Volume | 76 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 8 Aug 2007 |
Keywords
- fiber transmission-systems
- analytical design
- dispersion
- radiation
- solitons
Cite this
Exact analytical solutions for the variational equations derived from the nonlinear Schrodinger equation. / Moubissi, A. B.; Nakkeeran, K.; Abobaker, Abdosllam Moftah.
In: Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, Vol. 76, No. 2, 026603, 08.08.2007.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Exact analytical solutions for the variational equations derived from the nonlinear Schrodinger equation
AU - Moubissi, A. B.
AU - Nakkeeran, K.
AU - Abobaker, Abdosllam Moftah
PY - 2007/8/8
Y1 - 2007/8/8
N2 - By means of the variational formalism for the nonlinear Schrodinger equation, we find an explicit relation for the power of a pulse in terms of its duration, chirp and fiber parameters (group-velocity dispersion and self-phase modulation parameters). Then, using that relation, we derive the explicit analytical expressions for the variational equations corresponding to the amplitude, width, and chirp of the pulse. The derivation of the analytical expressions for the variational equations is possible for the condition when the Hamiltonian of the system is zero. Finally, for Gaussian and hyperbolic secant ansatz, we show good agreement between the results obtained from the analytical expressions and the direct numerical simulation of the nonlinear Schrodinger equation.
AB - By means of the variational formalism for the nonlinear Schrodinger equation, we find an explicit relation for the power of a pulse in terms of its duration, chirp and fiber parameters (group-velocity dispersion and self-phase modulation parameters). Then, using that relation, we derive the explicit analytical expressions for the variational equations corresponding to the amplitude, width, and chirp of the pulse. The derivation of the analytical expressions for the variational equations is possible for the condition when the Hamiltonian of the system is zero. Finally, for Gaussian and hyperbolic secant ansatz, we show good agreement between the results obtained from the analytical expressions and the direct numerical simulation of the nonlinear Schrodinger equation.
KW - fiber transmission-systems
KW - analytical design
KW - dispersion
KW - radiation
KW - solitons
U2 - 10.1103/PhysRevE.76.026603
DO - 10.1103/PhysRevE.76.026603
M3 - Article
VL - 76
JO - Physical Review. E, Statistical, Nonlinear and Soft Matter Physics
JF - Physical Review. E, Statistical, Nonlinear and Soft Matter Physics
SN - 1539-3755
IS - 2
M1 - 026603
ER -