论文标题
具有振幅依赖性wadati电势的非线性schrödinger方程
Nonlinear Schrödinger equations with amplitude-dependent Wadati potentials
论文作者
论文摘要
表格$ v（x）= - w^2（x） + iw_x（x）$的复杂wadati型电势，其中$ w（x）$是一个实现的功能，已知具有许多有趣的功能，对于通用的非官方潜力而言是不寻常的。在目前的工作中，我们引入了一类非线性schrödinger-type问题，通过假设基本函数$ w（x）$不仅取决于横向空间坐标，而且还取决于该领域的幅度，从而概括了wadati电位。讨论了前瞻性物理相关性的几个示例，包括具有非线性分散剂或衍生品非线性的模型。数值研究表明，广义模型继承了标准Wadati电位的显着特征，例如存在连续的孤子家族，当模型遵守平等时代对称性，恒定振幅波的存在时，可能会破坏对称性分叉的可能性，以及在linear demenvalue demeneal demeare quartets in the linear quartection interagity interearsibalsienty interagity spermainity insprability nepra ssstra。我们的结果加深了对非线性和非热性之间相互作用的当前理解，并扩展了系统类别的系统类别，这些系统享受着属性异常的异常组合，对于通用耗散性非线性模型而言。
Complex Wadati-type potentials of the form $V(x)=-w^2(x) + iw_x(x)$, where $w(x)$ is a real-valued function, are known to possess a number of intriguing features, unusual for generic non-Hermitian potentials. In the present work, we introduce a class of nonlinear Schrödinger-type problems which generalize the Wadati potentials by assuming that the base function $w(x)$ depends not only on the transverse spatial coordinate but also on the amplitude of the field. Several examples of prospective physical relevance are discussed, including models with the nonlinear dispersion or with the derivative nonlinearity. The numerical study indicates that the generalized model inherits the remarkable features of standard Wadati potentials, such as the existence of continuous soliton families, the possibility of symmetry-breaking bifurcations when the model obeys the parity-time symmetry, the existence of constant-amplitude waves, and the eigenvalue quartets in the linear-instability spectra. Our results deepen the current understanding of the interplay between nonlinearity and non-Hermiticity and expand the class of systems which enjoy the exceptional combination of properties unusual for generic dissipative nonlinear models.
