INVERSE SCATTERING TRANSFORM (IST) ANALYSIS OF KDV-BURGERS EQUATION

Inverse Scattering Transform (IST) method is applied to study a Korteweg-de Vries-Burgers' (KdV-Burgers') type equation due to Pramod and Vedan [Int. J. Non-Linear Mech. 27, 197-201 (1992)]. This equation represents long wave propagation in water where the depth changes, forming a shelf. The problem is formulated in terms of a Zakharov-Shabat eigenvalue system [Sov. Phys. JETP 34, 62-69 (1972)]. This study shows the excitation of a continuous spectrum and the evolution of new solitons. As an example the excitation of a continuous spectrum by one soliton as it passes the shelf is discussed.