Solitons in nonlinear systems and eigen-states in quantum wells<xref rid="cpb_28_1_010501fn1" ref-type="fn">*</xref> <fn id="cpb_28_1_010501fn1"> <label>*</label> <p>Project supported by the National Natural Science Foundation of China (Grant No. 11775176), the Basic Research Program of Natural Science of Shaanxi Province, China (Grant No. 2018KJXX-094), the Key Innovative Research Team of Quantum Many-Body Theory and Quantum Control in Shaanxi Province, China (Grant No. 2017KCT-12), and the Major Basic Research Program of Natural Science of Shaanxi Province, China (Grant No. 2017ZDJC-32).</p> </fn>

Solitons in nonlinear systems and eigen-states in quantum wells* *

Project supported by the National Natural Science Foundation of China (Grant No. 11775176), the Basic Research Program of Natural Science of Shaanxi Province, China (Grant No. 2018KJXX-094), the Key Innovative Research Team of Quantum Many-Body Theory and Quantum Control in Shaanxi Province, China (Grant No. 2017KCT-12), and the Major Basic Research Program of Natural Science of Shaanxi Province, China (Grant No. 2017ZDJC-32).

Zhao Li-Chen^{1, 2, †}, Yang Zhan-Ying^{1, 2}, Yang Wen-Li^{1, 2, 3}

The profiles of an asymmetric quantum double-well, for which it is hard to solve the Hamiltonian directly. But the corresponding eigen-state and eigenvalue can be obtained from the soliton solution of a nonlinear partial equation which is solved by Darboux transformation. The parameters are f = 1 and h = 2.