Kanna T, Vijayajayanthi M, Lakshmanan M
Post Graduate and Research Department of Physics, Bishop Heber College, Tiruchirapalli 620 017, India.
Department of Physics, Anna University, Chennai 600 025, India.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Oct;90(4):042901. doi: 10.1103/PhysRevE.90.042901. Epub 2014 Oct 1.
We derive a (2+1)-dimensional multicomponent long-wave-short-wave resonance interaction (LSRI) system as the evolution equation for propagation of N-dispersive waves in weak Kerr-type nonlinear medium in the small-amplitude limit. The mixed- (bright-dark) type soliton solutions of a particular (2+1)-dimensional multicomponent LSRI system, deduced from the general multicomponent higher-dimensional LSRI system, are obtained by applying the Hirota's bilinearization method. Particularly, we show that the solitons in the LSRI system with two short-wave components behave like scalar solitons. We point out that for an N-component LSRI system with N>3, if the bright solitons appear in at least two components, interesting collision behavior takes place, resulting in energy exchange among the bright solitons. However, the dark solitons undergo standard elastic collision accompanied by a position shift and a phase shift. Our analysis on the mixed bound solitons shows that the additional degree of freedom which arises due to the higher-dimensional nature of the system results in a wide range of parameters for which the soliton collision can take place.
我们推导了一个(2 + 1)维多分量长波-短波共振相互作用(LSRI)系统，作为N个色散波在弱克尔型非线性介质中传播的小振幅极限下的演化方程。通过应用广田双线性化方法，从一般的多分量高维LSRI系统推导出了一个特定的(2 + 1)维多分量LSRI系统的混合(亮-暗)型孤子解。特别地，我们表明具有两个短波分量的LSRI系统中的孤子表现得像标量孤子。我们指出，对于N > 3的N分量LSRI系统，如果亮孤子至少出现在两个分量中，就会发生有趣的碰撞行为，导致亮孤子之间的能量交换。然而，暗孤子经历标准的弹性碰撞，伴随着位置偏移和相位偏移。我们对混合束缚孤子的分析表明，由于系统的高维性质而产生的额外自由度导致了孤子碰撞能够发生的广泛参数范围。
