α-螺旋蛋白质中耦合非线性薛定谔方程高阶孤立波的动力学特性

Dynamic characteristics of higher-order solitary waves for the coupled nonlinear Schr?dinger equation in an alpha helical protein

在α-螺旋蛋白质中,非线性孤子的碰撞常被看作是传递能量的有效载体。基于一个描述α-螺旋蛋白质的耦合非线性薛定谔方程,利用经典Darboux变换,对函数进行泰勒展开,并用极限方法推导出N-1阶广义Darboux变换。在广义Darboux变换和已有Lax对的基础上,得到该方程N阶孤子解的表达式。分情况讨论谱参数λ的实部和虚部,选取不同的自由参数,研究参数对四孤子动力学行为的影响。通过数值模拟,给出四孤子相互作用的动力学演化图,并对四孤子的动力学特性进行分析。

In an alpha helical protein,the collision of nonlinear solitons is often regarded as an effective carrier for transmitting energy.In this paper,the coupled nonlinear Schr?dinger equations which describe an alpha helical protein are investigated.The Taylor expansion of the function is carried out via the classical Darboux transformation,and the generalized(N-1)th-order Darboux transformation is derived by using the limit method.Based on the generalized Darboux transformation and the existing Lax pair,the expression of the solutions of the Nth-order soliton is obtained.The real and imaginary parts of spectral parameter λ are discussed and different free parameters are selected to study the influence of parameters on the dynamic behavior of four-soliton.The dynamical evolution diagram of four-soliton interaction is given by numerical simulation,and the dynamical characteristics of four-soliton are analyzed.