Scarff II外势中广义导数非线性Schrodinger方程的精确解及其稳定性
Exact solutions of a generalized variant of the derivative nonlinear Schrodinger equation in a Scarff II external potential and their stability properties
摘要：
我们在Scarf-II势中得到了1+1维广义导数非线性薛定谔方程\equation的一个变体的精确孤波解，其中非线性参数$κ$为任意值.这个通常的衍生非线性薛定谔方程的变体具有这样的性质，即对于真实的外部势，动力学可以从拉格朗日导出。孤立波和陷波解的形式与通常的导数非线性薛定谔方程的形式相同。我们证明了$κ\leq 1$的孤立波解是轨道稳定的。我们发现了与方程静态解有关的外复势束缚态的新的精确无节点解。我们还使用集体坐标近似来分析当外部势为实时，被困解的稳定性。
英文摘要：
We obtain exact solitary wave solutions of a variant of the generalized derivative nonlinear Schrodinger\equation in 1+1 dimensions with arbitrary values of the nonlinearity parameter $κ$ in a Scarf-II potential. This variant of the usual derivative nonlinear Schrodinger equation has the properties that for real external potentials, the dynamics is derivable from a Lagrangian. The solitary wave and trapped solutions have the same form as those of the usual derivative nonlinear Schrodinger equation. We show that the solitary wave solutions are orbitally stable for $κ\leq 1$ We find new exact nodeless solutions to the bound states in the external complex potential which are related to the static solutions of the equation. We also use a collective coordinate approximation to analyze the stability of the trapped solutions when the external potential is real.
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