非线性系统访问的广义量子理论：利纳德和利文森-斯米斯方程的情况
Accessing Levinson-Smith and Liénard equations in a nonlinear framework of quantum mechanics
AI总结：
本文探讨了广义量子力学与非线性系统的关系，展示了利纳德方程可通过阿贝尔形式求解，而利文森-斯米斯方程与位置依赖质量系统相关，并产生类似孤子的解。
摘要：
我们展示了一种 recently introduced 的广义量子力学方案与利纳德和利文森-斯米斯类非线性系统之间的联系。对于具有奇数和奇数对称性的利纳德类型，我们证明通过转换到阿贝尔形式后可以得到闭合形式解。对于利文森-斯米斯方程，我们发现其与位置依赖质量系统相关，并且系统表面的条件导致类似孤子的解出现。
英文摘要：
In this paper, we present the reduction of a recently introduced generalized quantum scheme of Chodos and Cooper to Levinson-Smith and Liénard classes of nonlinear system that enable us to furnish a wider class of acceptable solutions. In particular, for the Levinson-Smith equations, we find their relevance to position-dependent mass quantum systems, with an interesting off-shoot that solitonic-like solutions emerge from the condition of the level surface in the system. On the other hand, for the Liénard type, which has coefficients of odd and odd symmetry in the present set up, we demonstrate that closed form solutions exist on carrying out conversion to the typical Abel form.
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