Nonlinear solitonic analogues of Schrödinger's cat states arise in the framework of the nonlinear Schrödinger equation (NLSE) model with confining harmonic oscillator potential. In-phase or out-of-phase displaced canonical(linear) Schrödinger's coherent states (well known as the “male” or “female” Schrödinger's cats) periodically oscillate and interfere in the crossing central point of confining harmonic oscillator potential. They are self-localized and robust linear solitary waves that do not disperse and preserve their identity after repeated collisions, and, in this sense, they are analogous to the well-known nonlinear bound states of the NLSE solitons. We discuss the main parallels and distinctions between canonical Schrödinger's cat states and their nonlinear solitonic analogues. Our primary aim is to reveal the main features of nonlinear solitonic analogues of Schrödinger's cat states restricted by the quantum-mechanical normalization condition and interpretation. The fulfillment of this condition means that, in general terms, the hypothesis of the possibility to develop nonlinear quantum mechanics can be tested directly by computational experiments with generalized NLSE models. We clarify how the strong short-range nonlinear forces lead to considerable decreasing (or increasing) of the oscillation periods between even and odd soliton-like Schrödinger's coherent states, when they closely approach each other. We demonstrate the possibility to realize the coherent superposition of practically noninteracting displaced solitonic Schrödinger's coherent states with opposite phases. Our analytical results do give a quite good qualitative and quantitative check of the numerical results known so far.

薛定ding猫状态的非线性声子类似物出现在非线性薛定ding方程（NLSE）模型的框架中，该方程具有约束谐波振荡器的势能。同相或异相位移正则（线性）薛定ding的相干态（众所周知的“雄性”或“雌性”薛定ding的猫）会周期性地振荡并干扰限定谐波振荡器电位的交叉中心点。它们是自定位且鲁棒的线性孤波，在反复碰撞后不会分散并保持其身份，从这个意义上讲，它们类似于NLSE孤子的众所周知的非线性束缚态。我们讨论了典型薛定ding猫状态与其非线性孤子声类似物之间的主要相似之处和区别。我们的主要目的是揭示受量子力学归一化条件和解释限制的薛定ding猫态的非线性孤子模拟的主要特征。满足此条件意味着，总的来说，可以通过使用广义NLSE模型进行的计算实验直接检验开发非线性量子力学可能性的假设。我们阐明了强短程非线性力如何在彼此接近时使偶数和奇数孤子形薛定ding相干态之间的振荡周期显着减小（或增大）。我们证明了有可能实现具有反相的几乎非互作用的位移孤子Schrödinger相干态的相干叠加。