ON THE NONINTEGRABLE HIROTA–SATSUMA SYSTEM OF COUPLED KdV EQUATIONS IN FLUID DYNAMICS

The coupled Korteweg-de Vries (KdV) equations are important in many fields, such as nonlinear optics, fluid dynamics, supersymmetry and so on. In this paper, we modify the recently proposed variable-coefficient balancing-act algorithm, and thus obtain some exact analytic solutions for the nonintegrable Hirota–Satsuma system of coupled KdV equations, which in fluid dynamics describe interactions of two long waves with different dispersion relations.