2019/12/23 by K. Krishnakumar, A. Durga Devi, Krishnakumar, K +5
Mathematics · Physics and Astronomy · #17B80 #34M15 #58J70 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1912.10624
openalex publication_date 2019/12/23 · openalex created_date 2019/12/26 · openalex updated_date 2026/07/28
We study the symmetry and integrability of a Generalized Modified Camassa-Holm Equation (GMCH) of the form ut-uxxt+2nux(u2-ux2)n-1(u-uxx)2+(u2-ux2)n(ux-uxxx)=0. We observe that for increasing values of n∈ ℕ, ℕ denotes natural number, the above equation gives a family of equations in which nonlinearity is rapidly increasing as n increases. However, this family has similar form of symmetries except the values of n. Interestingly the resultant second-order nonlinear ODE which is to be obtained from GMCH equation has eight dimensional symmetries. Hence the second-order nonlinear ODE is linearizable. Finally we conclude that the resultant second-order nonlinear ordinary differential equation which is obtained from the family of GMCH passes the Painlevé Test also it posses the similar form of leading order, resonances and truncated series solution too.