31 research outputs found
Coherently coupled bright optical solitons and their collisions
We obtain explicit bright one- and two-soliton solutions of the integrable case of the coherently coupled nonlinear Schrödinger equations by applying a non-standard form of Hirota's direct method. We find that the system admits both degenerate and non-degenerate solitons in which the latter can take single-hump, double-hump and flat-top profiles. Our study on the collision dynamics of solitons in the integrable case shows that the collision among degenerate solitons and the collision among non-degenerate solitons are always standard elastic collisions. But the collision of a degenerate soliton with a non-degenerate soliton induces switching in the latter leaving the former unaffected after collision, thereby showing a different mechanism from that of the Manakov system
Simulation of universal optical logic gates under energy sharing collisions of Manakov solitons and fulfillment of practical optical logic criteria
The universal optical logic gates, namely NAND and NOR gates, have been
theoretically simulated by employing the energy sharing collision of bright
optical solitons in the Manakov system, governing pulse propagation in a highly
birefringent fiber. Further, we also realize the two input optical logic gates
such as AND, OR, XOR, XNOR for completeness of our scheme. Interestingly, our
idea behind the simulation naturally satisfies all the criteria for practical
optical logic which in turn displays the strength and versatility of our
theoretical simulation of universal optical logic gates. Hence, our approach
paves the way for the experimentalists to create a new avenue in this direction
if the energy sharing collisions of Manakov solitons are experimentally
realized in the future.Comment: 7 figures. arXiv admin note: substantial text overlap with
arXiv:1806.0096
Bright-dark solitons and their collisions in mixed N-coupled nonlinear Schr\"odinger equations
Mixed type (bright-dark) soliton solutions of the integrable N-coupled
nonlinear Schr{\"o}dinger (CNLS) equations with mixed signs of focusing and
defocusing type nonlinearity coefficients are obtained by using Hirota's
bilinearization method. Generally, for the mixed N-CNLS equations the bright
and dark solitons can be split up in ways. By analysing the collision
dynamics of these coupled bright and dark solitons systematically we point out
that for , if the bright solitons appear in at least two components,
non-trivial effects like onset of intensity redistribution, amplitude dependent
phase-shift and change in relative separation distance take place in the bright
solitons during collision. However their counterparts, the dark solitons,
undergo elastic collision but experience the same amplitude dependent
phase-shift as that of bright solitons. Thus in the mixed CNLS system there
co-exist shape changing collision of bright solitons and elastic collision of
dark solitons with amplitude dependent phase-shift, thereby influencing each
other mutually in an intricate way.Comment: Accepted for publication in Physical Review
Higher dimensional bright solitons and their collisions in multicomponent long wave-short wave system
Bright plane soliton solutions of an integrable (2+1) dimensional
()-wave system are obtained by applying Hirota's bilinearization method.
First, the soliton solutions of a 3-wave system consisting of two short wave
components and one long wave component are found and then the results are
generalized to the corresponding integrable ()-wave system with short
waves and single long wave. It is shown that the solitons in the short wave
components (say and ) can be amplified by merely reducing
the pulse width of the long wave component (say L). The study on the collision
dynamics reveals the interesting behaviour that the solitons which split up in
the short wave components undergo shape changing collisions with intensity
redistribution and amplitude-dependent phase shifts. Even though similar type
of collision is possible in (1+1) dimensional multicomponent integrable
systems, to our knowledge for the first time we report this kind of collisions
in (2+1) dimensions. However, solitons which appear in the long wave component
exhibit only elastic collision though they undergo amplitude-dependent phase
shifts.Comment: Published in J. Phys. A Math. Theo