论文标题
崩溃发作的一种正常形式：非线性schrodinger方程的原型示例
A Normal Form for the Onset of Collapse: the Prototypical Example of the Nonlinear Schrodinger Equation
论文作者
论文摘要
在有限时间崩溃的非线性波的研究是普遍利益的主题，例如在光学，原子，等离子体物理和非线性动力学中。在这里，我们重新审视了非线性schrodinger方程的典型示例，并系统地得出了从固定固定溶液出现爆炸溶液的正常形式。尽管这是一个广泛研究的问题，但这种正常形式，基于除所有代数顺序以外的渐近方法的方法，统一了先前研究的维度依赖性和依赖性依赖性分歧。它与数字在领导和高阶效应中产生了极好的一致性。它适用于无限和有限域。它在所有（次临界，批判性和超批评）方面都是有效的。
The study of nonlinear waves that collapse in finite time is a theme of universal interest, e.g. within optical, atomic, plasma physics, and nonlinear dynamics. Here we revisit the quintessential example of the nonlinear Schrodinger equation and systematically derive a normal form for the emergence of blowup solutions from stationary ones. While this is an extensively studied problem, such a normal form, based on the methodology of asymptotics beyond all algebraic orders, unifies both the dimension-dependent and power-law-dependent bifurcations previously studied; it yields excellent agreement with numerics in both leading and higher-order effects; it is applicable to both infinite and finite domains; and it is valid in all (subcritical, critical and supercritical) regimes.
