Scholarlink

Abstract <p>The article is devoted to the development of S.A. Lomov’s regularization method for singularly perturbed problems in the presence of spectral singularities in the limit operator. In particular, a regularized asymptotic solution to the singularly perturbed Cauchy problem for the Schrödinger equation is constructed on time intervals containing focal points. Based on the ideas of asymptotic integration of problems with an unstable spectrum, it is indicated how regularizing functions should be introduced, the formalism of the regularization method for the specified type of singularity is described in detail, the justification of this algorithm is carried out and an asymptotic solution of any order with respect to a small parameter is constructed.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Regularized Asymptotics of the Solution of the Singularly Perturbed Cauchy Problem for the Homogeneous Schrödinger Equation with the Potential \(\boldsymbol{Q=X^{2}}\) Containing Focal Points

  • 期刊论文

  • 发表日期：

    2025年7月1日

查看全文
  • A. G. Yeliseev,
  • T. A. Ratnikova,
  • D. A. Shaposhnikova

摘要

Abstract

The article is devoted to the development of S.A. Lomov’s regularization method for singularly perturbed problems in the presence of spectral singularities in the limit operator. In particular, a regularized asymptotic solution to the singularly perturbed Cauchy problem for the Schrödinger equation is constructed on time intervals containing focal points. Based on the ideas of asymptotic integration of problems with an unstable spectrum, it is indicated how regularizing functions should be introduced, the formalism of the regularization method for the specified type of singularity is described in detail, the justification of this algorithm is carried out and an asymptotic solution of any order with respect to a small parameter is constructed.