EXACT SOLUTIONS FOR THE NONISOSPECTRAL LOADED KORTEWEG-DE VRIES EQUATION VIA INVERSE SCATTERING TRANSFORM

Abstract

In this paper, soliton-like solutions for the Korteweg–de Vries (KdV) equation with variable
coefficients are investigated using the Inverse Scattering Transform (IST) method. By applying appropriate
transformations, the original equation is reduced to an integrable form. Subsequently, new general soliton
solutions of the resulting equation are derived via the IST method, and explicit analytical solutions are
obtained in closed form. The proposed approach can be effectively extended to analyze other classes of
integrable nonlinear systems.