The existence of soliton families in nonparity-time-symmetric complex potentials remains poorly understood, especially in two spatial dimensions. In this article, we analytically investigate the bifurcation of soliton families from linear modes in one- and two-dimensional nonlinear Schrödinger equations with localized Wadati-type nonparity-time-symmetric complex potentials. By utilizing the conservation law of the underlying non-Hamiltonian wave system, we convert the complex soliton equation into a new real system. For this new real system, we perturbatively construct a continuous family of low-amplitude solitons bifurcating from a linear eigenmode to all orders of the small soliton amplitude. Hence, the emergence of soliton families in these nonparity-time-symmetric complex potentials is analytically explained. We also compare these analytically constructed soliton solutions with high-accuracy numerical solutions in both one and two dimensions, and the asymptotic accuracy of these perturbation solutions is confirmed.

中文翻译：

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具有非奇偶时间对称复势的一维和二维非线性薛定谔方程中孤子族的解析构造

对非奇偶时间对称复势中孤子族的存在仍然知之甚少，尤其是在两个空间维度中。在本文中，我们分析研究了具有局部瓦达蒂型非奇偶时间对称复势的一维和二维非线性薛定谔方程中线性模式的孤子族的分岔。利用潜在的非汉密尔顿波系统的守恒定律，我们将复杂的孤子方程转换为一个新的真实系统。对于这个新的真实系统，我们微扰地构建了一个连续的低振幅孤子族，从线性本征模式分叉到小孤子振幅的所有阶。因此，分析解释了这些非奇偶时间对称复势中孤子族的出现。