玻色化方法在超对称可积系统的应用

Bosonization approach for supersymmetric integrable system

利用玻色化方法可以避免超对称可积系统中反对易费米场带来的计算困难.本文以N=1超对称mKdVB系统为例,利用玻色化方法,将其转化为只有玻色场的耦合系统.应用标准的WTC方法,证明了该耦合系统具有Painlevé性质.运用Painlevé截断方法,可以得到玻色化后超对称mKdVB系统的非局域对称.为了求解与非局域对称相关的Lie第一性原理,引入新的场将玻色化后系统拓展为更大的系统.通过引入新的场,该非局域对称局域化为Lie点对称.因此,可以利用Lie点对称约化方法研究拓展后的系统,得到超对称mKdVB系统的孤子与其他孤波相互作用解.

To address the difficulty caused by the anti-commutative fermionic fields,a bosonization approach is proposed to deal with the super-symmetric integrable systems.The N=1 super-symmetric mKdVB system is transformed to a coupled bosonic system using the bosonization approach.Adopting a standard WTC approach,the bosonized super-symmetric mKdVB(BSmKdVB)equation possesses the Painlevéproperty.Starting from the standard truncated Painlevémethod,the nonlocal symmetry for the BSmKdVB equation is obtained.To solve the first Lie’s principle related with the nonlocal symmetry,the nonlocal symmetry is localized to the Lie point symmetry by introducing multiple new fields.By taking advantage of localization processes,similarity reductions for the prolonged systems can be studied using the Lie point symmetry method.The interaction solutions for solitons and other complicated waves are presented using the reduction method.