Exact solutions of (1 + 1)-dimensional integro-differential Ito, KP hierarchy, CBS, MCBS and modified KdV-CBS equations

• Published in: PloS one Vol. 18; no. 3; p. e0283569
• Main Authors: Amin, Amina, Naeem, Imran, Khan, Adnan
• Format: Journal Article
• Language: English
• Published: United States Public Library of Science 30.03.2023; Public Library of Science (PLoS)
• Subjects: Algorithms; Applied mathematics; Biology and Life Sciences; Computer and Information Sciences; Data mining; Dependent variables; Differential equations; Engineering and Technology; Evaluation; Exact solutions; Independent variables; Nonlinear differential equations; Nonlinear equations; Partial differential equations; Physical Sciences; Physics; Short Interspersed Nucleotide Elements; Similarity; Symmetry; Trigonometric functions; Pakistan
• ISSN: 1932-6203; 1932-6203
• DOI: 10.1371/journal.pone.0283569

The present study computes the Lie symmetries and exact solutions of some problems modeled by nonlinear partial differential equations. The (1 + 1)-dimensional integro-differential Ito, the first integro-differential KP hierarchy, the Calogero-Bogoyavlenskii-Schiff (CBS), the modified Calogero-Bogoyavlenskii-Schiff (CBS), and the modified KdV-CBS equations are some of the problems for which we want to find new exact solutions. We employ similarity variables to reduce the number of independent variables and inverse similarity transformations to obtain exact solutions to the equations under consideration. The sine-cosine method is then utilized to determine the exact solutions.