Exact solutions of Calgero–Bogoyavlenskii–Schiff equation using the singular manifold method after Lie reductions. (17th May 2017)

• Record Type: Journal Article
• Authors: Saleh, R.; Kassem, M.; Mabrouk, S.
• Is Part Of: Mathematical methods in the applied sciences. Volume 40:Number 16(2017)
• Page Start: 5851
• Page End: 5862
• Publication Date: 2017-05-17
• Subjects: Calogero–Bogoyavlenskii–Schiff equation -- similarity transformation -- singular manifold method -- Schwarzian derivative -- Bäcklund transformations; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4435
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : Calgero–Bogoyavlenskii–Schiff (CBS) equation is analytically solved through two successive reductions into an ordinary differential equation (ODE) through a set of optimal Lie vectors. During the second reduction step, CBS equation is reduced using hidden vectors. The resulting ODE is then analytically solved through the singular manifold method in three steps; First, a Bäcklund truncated series is obtained. Second, this series is inserted into the ODE, and finally, a seminal analysis leads to a Schwarzian differential equation in the eigenfunction φ ( η ). Solving this differential equation leads to new analytical solutions. Then, through two backward substitution steps, the original dependent variable is recovered. The obtained results are plotted for several Lie hidden vectors and compared with previous work on CBS equation using Lie transformations. Copyright © 2017 John Wiley & Sons, Ltd.