Author : Steven Ivan Dejak
Publisher :
ISBN 13 : 9780494219140
Total Pages : 158 pages
Book Rating : 4.2/5 (191 download)
Book Synopsis Long-time Dynamics of Korteweg-de Vries Solitary Waves Over a Variable Bottom by : Steven Ivan Dejak
Download or read book Long-time Dynamics of Korteweg-de Vries Solitary Waves Over a Variable Bottom written by Steven Ivan Dejak and published by . This book was released on 2006 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the dynamics of solitons of KdV-type equations arising in the theory of shallow water waves propagating over channels with variable bottom. Under a rescaling, these waves satisfy the variable bottom generalized Korteweg-de Vries (bKdV) equation & part;tu = - & part;x(62x u + f(u) - b(t, x)u) with f = u2 and b related to the varying channel depth. The main result of the thesis is concerned with solitary wave dynamics of the bKdV with f a general nonlinearity (modulo some constraints) and b a small, bounded and slowly varying function. We prove that under suitable conditions on b and f, the bKdV is globally well-posed. With the knowledge that solutions exist, we study the long time behaviour of solutions with initial conditions close to a stable, b = 0 solitary wave. We prove that for long time intervals, such solutions have the form of a solitary wave, whose centre and scale evolve according to a certain dynamcal law involving the function b(t, x), plus an H 1(R)-small fluctuation. As motivation, we also describe how the bKdV equation appears in the field of water waves.