Numerical Investigation of Fractional Kawahara Equation via Haar Scale Wavelet Method

The Kawahara equation is a fifth-order dispersive equation that plays a significant role in explaining the creation of non-linear water waves in the long-wavelength region. In this research, the Kawahara equation is solved numerically using the novel Haar scale-3 wavelet method in conjunction with the collocation method. The quasilinearisation approach and the Caputo derivative are used to characterise the non-linearity and fractional behaviour of the equation, respectively. To verify that the findings obtained are legitimate, residual and error estimates are generated. A thorough comparison is made between the present solutions and the numerical findings that have already been published in the literature, which demonstrates the advantages and effectiveness of the suggested technique. The Haar wavelet method reveals a dynamic system of alternative solutions for a wide variety of physical parameters.