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

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.

► The problem with a lax pair spectral representation of Eq. (1.1).
► This lax Pair is similarly reduced using the group method.
► Three similarity variables are detected.
► The coefficients of the spectral function ψ(x, y, z) and derivatives are compared in the reduced lax pair system.
► Peakon solutions are obtained.