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 correspondence between eigen-states in the quantum well and non-degenerated solitons in 4-component coupled NLS with attractive interactions or repulsive interactions. Panels (a1)–(a4) show the evolution of solitons in the four components with attractive interactions, respectively. Panels (b1)–(b4) show the first four eigen-states in the quantum well − 6 f sech 2 [ f x ] . Panels (c1)–(c4) show the evolution of solitons in the four components with repulsive interactions, respectively. It is shown that the density profiles of soliton correspond to the eigen-states precisely. The solitons in attractive case have different amplitudes from the ones in repulsive cases, but they admit identical eigenvalues in the quantum well. The parameters in soliton solutions are a = 1 and f = 1.