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By employing an inverse-scattering transformation, the exact solution of an N-soliton train in the spin chain with a time-dependent magnetic field is derived. As a special case the one-soliton solution (N = 1) exhibits explicitly the spin precession around the magnetic field and periodic shape-variation induced by the time varying field as well. In terms of the general solution, inelastic two-soliton collision is analysed. The inelastic collision, by which we mean the soliton shape-change before and after collision, appears generally due to the time varying field. 相似文献
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Higher-order nonlinear Schr\"{o}dinger equation with the Hirota
constraint conditions is considered, and an analytic solution, which
can describe the modulational instability process, is presented.
Based on the solution, a new pulse train without continuous wave (CW)
background is generated in quadratures and the propagation of the
pulse train is discussed in detail by simulating numerically. The
results show that, unlike the propagation of the picosecond pulse
train, under the effects of the higher-order terms, the pulse train
cannot propagate along the fibre when the energy is very high;
however, for some medium energy the pulse train can stably propagate.
We also investigate the stability of the pulse train against
violation of the Hirota conditions, and the results show that the
pulse train can still propagate stably when the Hirota conditions are
broken. 相似文献
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This paper investigates the adjacent interactions of three novel solitons for the
quintic complex Ginzburg--Landau equation, which are plain pulsating,
erupting and creeping solitons. It is found that different
performances are presented for different solitons due to isolated regions of
the parameter space where they exist. For example, plain pulsating and
erupting solitons exhibit mutual annihilation during collisions with the
decrease of total energy, but for creeping soliton, the two adjacent
pulses present soliton fusion without any loss of energy. Otherwise, the
method for restraining the interactions is also found and it can suppress
interactions between these two adjacent pulses effectively. 相似文献
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Theory of passively mode-locked lasers with self-frequency shift and saturable absorber response 下载免费PDF全文
A general theoretical model for passively mode-locked lasers is presented, in which both the self-frequency shift and either a fast or a slow saturable absorber response are taken into account. An exact soliton-like solution and condition for its existence are obtained under a definite compatible condition. The stability of the solution is analyzed by using a variational method, and a parameter region, in which the solution is linearly stable, is acquired theoretically. To verify the theoretical predictions, a typical example is given for stable pulse propagation over a long distance. The numerical results show that the soliton-like solution is stable under some perturbations within the linearly stable region and an arbitrary Gaussian pulse converges to the exact soliton-like solution after evolution in a distance. 相似文献
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The Lax pair given for the equations of motion of a continuum-Heisenberg-spin chain of an easy axis in an oscillating magnetic field.Using an inverse scattering transformation we derive soliton solutions for the case of the easy axis. 相似文献
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In this letter, exact chirped multi-soliton solutions of the nonlinear Schrodinger (NLS) equation with varying coefficients are found. The explicit chirped one- and two-soliton solutions are generated. As an example, an exponential distributed control system is considered, and some main features of solutions are shown. The results reveal that chirped soliton can all be nonlinearly compressed cleanly and efficiently in an optical fiber with no loss or gain, with the loss, or with the gain. Furthermore, under the same initial condition, compression of optical soliton in the optical fiber with the loss is the most dramatic. Also, under nonintegrable condition and finite initial perturbations, the evolution of chirped soliton has been demonstrated by simulating numerically. 相似文献
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