Solitons and Resonance in Fractional Sawada-Kotera Equation Using Hirota Bilinear Method

The resonance of non-linear waves are studied in the fractional Sawada-Kotera (FSK) equation using Hirota bilinear method. All the mathematical calculations are done using symbolic computation. The effects of fractional order parameter ( \(\alpha \) ) are shown graphically on one-soliton and two-soliton solutions. In one-soliton solution the change of phase is prominent with the enhancement of \(\alpha \) . It is significant to note that, when the phase shift parameter ( \(\beta _{12}\) ) tends to zero or infinity, two-soliton solution exhibits the behavior of resonance. At resonant state, a soliton splits into two-soliton or two-soliton fuses and is transmuted into singular soliton.