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Math. Anal."],"published-print":{"date-parts":[[2026,6,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>This paper is concerned with the inverse scattering problem of determining the unknown potential for the classical Schr\u00f6dinger equation in two and three dimensions. For the first time, increasing stability estimates of the inverse scattering problem are achieved from either multi-wavenumber near-field or far-field data. The stability estimate consists of two parts: one part is the Lipschitz stability,\u00a0and the other part is the logarithmic stability. As the wavenumber increases, the logarithmic part decreases and the stability approaches a Lipschitz stability. The increasing stability estimate reveals that ill-posedness of the inverse problems can be overcome by the use of multi-wavenumber data. With multi-wavenumber data, the analysis does not resort to the construction of CGO solutions and thus can be used to deal with the two-dimensional case. A key ingredient in the analysis is employing scattering theory to obtain an analytic region and estimates in this region for the resolvent of the elliptic operator. This method is further utilized to investigate the inverse scattering problem of determining both the magnetic and the electric potentials for the magnetic Schr\u00f6dinger equation. This problem is more challenging due to the nonlinearity and first-order perturbation.<\/jats:p>","DOI":"10.1137\/25m1767108","type":"journal-article","created":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T07:40:51Z","timestamp":1777880451000},"page":"2111-2137","source":"Crossref","is-referenced-by-count":0,"title":["Stability for the Inverse Potential Scattering Problems with Multi-Wavenumbers"],"prefix":"10.1137","volume":"58","author":[{"given":"Gang","family":"Bao","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Zhejiang University, Hangzhou, 310027 China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2374-8922","authenticated-orcid":true,"given":"Jian","family":"Zhai","sequence":"additional","affiliation":[{"name":"School of Mathematical Science, Fudan University, Shanghai, 200433 China, and Center for Applied Mathematics, Fudan University, Shanghai, 200433, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yue","family":"Zhao","sequence":"additional","affiliation":[{"name":"Corresponding author. 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