Multi-resolution wavelet basis for solving steady forced Korteweg–de Vries model

Abstract A steady forced Korteweg–de Vries (fKdV) model which includes gravity, capillary, and pressure distributions is solved numerically using the wavelet Galerkin method. The anti-derivatives of Daubechies wavelets are developed as basis solution subspaces for mixed boundary condition type. Accuracy numerical solutions can be improved by increasing number levels in multi-resolution analysis. theoretical result convergence rate also shown. problem viewed gravity-capillary wave flows over an applied distribution. flow regime characterized subcritical, supercritical, critical depending on value Froude number. Trapped depression elevation waves found For a near-critical regime, generalized solitary with ripples presented. This shows capillary effect balance to gravity force free surface.