{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,4]],"date-time":"2026-02-04T11:02:08Z","timestamp":1770202928437,"version":"3.49.0"},"reference-count":19,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["New Math. and Nat. Computation"],"published-print":{"date-parts":[[2026,9]]},"abstract":"<jats:p>A new generalized Fisher\u2013Kolmogorov\u2013Petrovskii\u2013Piskunov equation [Formula: see text] is introduced and subjected to Lie\u2019s Classical Method to establish the existence of the traveling waves. Indeed, exact expressions for both the solution [Formula: see text], with [Formula: see text] and the wave speed [Formula: see text] are subsequently derived by the regular perturbation method and are shown to contain both the reports of Ablowitz and Zeppetella [Explicit solutions of fisher\u2019s equation for a special wave speed, Bulletin of Mathematical Biology\u00a041(6) (1979) 835\u2013840] when [Formula: see text] and Kaliappan [An exact solution for the traveling waves of [Formula: see text], Physica D: Nonlinear Phenomena\u00a011(3) (1984) 368\u2013374] when [Formula: see text], respectively. Remarkably, the generalized Huxley equation is a special case of our model equation. The form of the traveling waves for the Fisher\u2013Kolmogorov\u2013Petrovskii\u2013Piskunov equations is identified with the regular perturbation method and the Binomial series. Our study is in agreement with the conclusion of Fisher [The wave of advance of advantageous genes, Annals of Eugenics\u00a07(4) (1937) 355\u2013369] that the increase of frequency of mutant genes results in the diffusion of the mutant genes into the long range.<\/jats:p>","DOI":"10.1142\/s1793005726500419","type":"journal-article","created":{"date-parts":[[2025,1,3]],"date-time":"2025-01-03T05:05:41Z","timestamp":1735880741000},"page":"845-862","source":"Crossref","is-referenced-by-count":0,"title":["A Boundary Value Problem for Algebraically Accelerated Frequency of Mutations Governed by Fisher\u2013Kolmogorov\u2013Petrovskii\u2013Piskunov Equation"],"prefix":"10.1142","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-9088-0789","authenticated-orcid":false,"given":"Anitha","family":"Ponraj","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics and Statistics, Madurai Kamaraj University, Madurai 625021, Tamil Nadu, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1474-0320","authenticated-orcid":false,"given":"B.","family":"Mayil Vaganan","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics and Statistics, Madurai Kamaraj University, Madurai 625021, Tamil Nadu, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2025,2,5]]},"reference":[{"key":"S1793005726500419BIB001","doi-asserted-by":"publisher","DOI":"10.1111\/j.1469-1809.1937.tb02153.x"},{"key":"S1793005726500419BIB002","first-page":"1","volume":"1","author":"Kolmogorov A.","year":"1937","journal-title":"Bulletin Universit\u00e9 d\u2019\u00c9 tat \u00e0 Moscou"},{"key":"S1793005726500419BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/b98868"},{"key":"S1793005726500419BIB004","volume-title":"Elements of Mathematical Ecology","author":"Kot M.","year":"2003"},{"key":"S1793005726500419BIB005","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719147"},{"key":"S1793005726500419BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/S0092-8240(79)80020-8"},{"key":"S1793005726500419BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(82)90001-4"},{"key":"S1793005726500419BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(84)90018-6"},{"key":"S1793005726500419BIB009","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/23\/3\/011"},{"key":"S1793005726500419BIB010","volume-title":"Group Analysis of Differential Equations","author":"Ovsiannikov L. 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