Quintero Niurka R, Mertens Franz G, Bishop A R
Departamento de Física Aplicada I, EUP, Universidad de Sevilla, Sevilla, Spain.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Jul;82(1 Pt 2):016606. doi: 10.1103/PhysRevE.82.016606. Epub 2010 Jul 29.
The generalized traveling wave method (GTWM) is developed for the nonlinear Schrödinger equation (NLSE) with general perturbations in order to obtain the equations of motion for an arbitrary number of collective coordinates. Regardless of the particular ansatz that is used, it is shown that this alternative approach is equivalent to the Lagrangian formalism, but has the advantage that only the Hamiltonian of the unperturbed system is required, instead of the Lagrangian for the perturbed system. As an explicit example, we take 4 collective coordinates, namely the position, velocity, amplitude and phase of the soliton, and show that the GTWM yields the same equations of motion as the perturbation theory based on the Inverse Scattering Transform and as the time variation of the norm, first moment of the norm, momentum, and energy for the perturbed NLSE.
为了获得任意数量集体坐标的运动方程，针对具有一般微扰的非线性薛定谔方程（NLSE）开发了广义行波方法（GTWM）。无论使用何种特定假设，都表明这种替代方法等同于拉格朗日形式，但具有仅需要未微扰系统的哈密顿量而非微扰系统的拉格朗日量这一优点。作为一个具体例子，我们采用4个集体坐标，即孤子的位置、速度、幅度和相位，并表明GTWM产生的运动方程与基于逆散射变换的微扰理论以及与微扰NLSE的范数、范数的一阶矩、动量和能量的时间变化所得到的运动方程相同。
