Group similarity solutions of the lax pair for a generalized Hirota–Satsuma equation

摘要

A modified version of generalized Hirota–Satsuma is here analytically solved using a two parameter group transformation method. We here through a Group symmetry transformation reduce its lax pair to a system of ordinary equations and find new solutions. Three similarity transformation variables are investigated. For each case an analytical solution is obtained through a homogenous balance of terms in the reduced lax pair. The obtained results are plotted and show a profile proper to deflagration processes, well described by Degasperis–Procesi equation.