Christian J M, McDonald G S, Chamorro-Posada P
Joule Physics Laboratory, School of Computing, Science and Engineering, Institute for Materials Research, University of Salford, Salford M5 4WT, UK.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Dec;74(6 Pt 2):066612. doi: 10.1103/PhysRevE.74.066612. Epub 2006 Dec 28.
A different spatial soliton-bearing wave equation is introduced, the Helmholtz-Manakov (HM) equation, for describing the evolution of broad multicomponent self-trapped beams in Kerr-type media. By omitting the slowly varying envelope approximation, the HM equation can describe accurately vector solitons propagating and interacting at arbitrarily large angles with respect to the reference direction. The HM equation is solved using Hirota's method, yielding four different classes of Helmholtz soliton that are vector generalizations of their scalar counterparts. General and particular forms of the three invariants of the HM system are also reported.
引入了一个不同的含空间孤子波动方程，即亥姆霍兹 - 马纳科夫（HM）方程，用于描述克尔型介质中宽多分量自陷光束的演化。通过省略缓变包络近似，HM方程可以精确描述相对于参考方向以任意大角度传播和相互作用的矢量孤子。使用广田方法求解HM方程，得到了四类不同的亥姆霍兹孤子，它们是其标量对应物的矢量推广。还报道了HM系统三个不变量的一般形式和特殊形式。
