1-Soliton solution and conservation laws for the Jaulent-Miodekequation with power law nonlinearity
Abstract This paper obtains the 1-soliton solution of the Jaulent–Miodek equation with power law nonlinearity. The solitary wave ansatz is used to obtain the soliton solution to this equation. Subsequently, the conserved quantities are computed using the invariance and multiplier approach based on the well known result that the Euler–Lagrange operator annihilates the total divergence.
Hidden symmetries and exact solutions of integro-differential Jaulent-Miodek evolution equation
Use of the adjoint method, to obtain optimal Lie vectors.A reduction of the JM equation to ordinary differential equations and detection of Lie symmetries.Test if these symmetries are hidden.Analysis and plot of results.Comparison with previous work in the field. Analytical solutions of a '(2+1)' dimensional nonlinear model using the Jaulent-Miodek hierarchy are investigated following a similarity reduction procedure. For this adjoint Lie matrices are first evaluated and an extensive list of optimal Lie vectors is obtained. The systematic reduction of Jaulent-Miodek evolution equation to lower number of variables leads to hidden symmetries and new solutions.
Coherent pulsed injection seeding of two gain-switched semiconductor lasers
High-power, narrow-spectrum, short pulses at a wavelength near 830 nm are needed for optical logic applications. The authors report the generation of two coherent trains of pulses by pulsed injection seeding of two gain-switched semiconductor lasers with one mode-locked master oscillator. The available power was doubled and both lasers emit in nearly identical spectral lines. Short pulses (30-50 ps) are generated at a repetition rate of 1.9 GHz. The spectrum is reduced to a single mode cluster and shows a 1.7 AA wide chirp suitable for pulse compression. The peak power is 0.1 W for each pulse train. The capability of this technique for coherent power combining is demonstrated.<<ETX>>