Abstract
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.
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