{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:06:16Z","timestamp":1760058376936,"version":"build-2065373602"},"reference-count":44,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,3,28]],"date-time":"2025-03-28T00:00:00Z","timestamp":1743120000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Beijing Natural Science Foundation","award":["1222005","MS2024378"],"award-info":[{"award-number":["1222005","MS2024378"]}]},{"name":"2024 Project of the Beijing Higher Education Society","award":["1222005","MS2024378"],"award-info":[{"award-number":["1222005","MS2024378"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This study investigates the (2+1)-dimensional asymmetric Nizhnik\u2013Novikov\u2013Veselov (ANNV) equation, a significant model in nonlinear science, using the Kadomtsev\u2013Petviashvili (KP) hierarchy reduction method. Despite the extensive research on the ANNV equation, a comprehensive exploration of its solutions using the KP hierarchy reduction method is lacking. This gap is addressed by identifying constraint conditions that transform a specific KP hierarchy equation into the ANNV equation, thereby enabling the derivation of its Gram determinant solutions. By selecting appropriate \u03c4 functions, we obtain breather solutions and analyze their dynamic behavior during wave oscillations. Additionally, lump solutions are derived through long-wave limit analysis, revealing their unique characteristics. This study further explores hybrid solutions that combine breathers and lumps, providing new insights to the interaction between these localized wave phenomena. Our findings enhance the understanding of the ANNV equation\u2019s dynamics and contribute to the broader field of nonlinear wave theory.<\/jats:p>","DOI":"10.3390\/sym17040514","type":"journal-article","created":{"date-parts":[[2025,3,28]],"date-time":"2025-03-28T13:36:49Z","timestamp":1743169009000},"page":"514","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Characteristic Analysis of Local Wave Solutions for the (21)-Dimensional Asymmetric Nizhnik\u2013Novikov\u2013Veselov Equation"],"prefix":"10.3390","volume":"17","author":[{"given":"Jingyi","family":"Chu","sequence":"first","affiliation":[{"name":"School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6354-5401","authenticated-orcid":false,"given":"Yaqing","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China"}]},{"given":"Huining","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Science, Shijiazhuang University, Shijiazhuang 050035, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5035-3555","authenticated-orcid":false,"given":"Manwai","family":"Yuen","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Information Technology, The Education University of Hong Kong, Lo Ping Road, Tai Po, New Territories, Hong Kong, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Ablowitz, M.J., and Clarkson, P.A. 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