2001
DOI: 10.1016/s0378-4754(00)00294-9
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Propagation of axi-symmetric nonlinear shallow water waves over slowly varying depth

Abstract: A problem in nonlinear water-wave propagation on the surface of an inviscid, stationary fluid is presented.The primary surface wave, suitably initiated at some radius, is taken to be a slowly evolving nonlinear cylindrical wave (governed by an appropriate Korteweg-de Vries equation); the depth is assumed to be varying in a purely radial direction.We consider a sech 2 profile at an initial radius (which is, following our scalings, rather large), and we describe the evolution as it propagates radially outwards. … Show more

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Cited by 6 publications
(3 citation statements)
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“…Mass “leaks” into this shelf, so there is an inherent dissipation associated with the spreading. The leading order term, or primary wave, in a suitable expansion looking for such solutions is [ Grimshaw , ; Killen and Johnson , ]: η=B0false(r/r0false)2/3sech2true{μB012δfalse(r/r0false)2/3true(rr0c0tμB0r0c0true(false(r/r0false)1/31true)true)true} where the initial wave amplitude at a distance r 0 is B 0 .…”
Section: Discussionmentioning
confidence: 99%
See 1 more Smart Citation
“…Mass “leaks” into this shelf, so there is an inherent dissipation associated with the spreading. The leading order term, or primary wave, in a suitable expansion looking for such solutions is [ Grimshaw , ; Killen and Johnson , ]: η=B0false(r/r0false)2/3sech2true{μB012δfalse(r/r0false)2/3true(rr0c0tμB0r0c0true(false(r/r0false)1/31true)true)true} where the initial wave amplitude at a distance r 0 is B 0 .…”
Section: Discussionmentioning
confidence: 99%
“…Mass ''leaks'' into this shelf, so there is an inherent dissipation associated with the spreading. The leading order term, or primary wave, in a suitable expansion looking for such solutions is [Grimshaw, 1998;Killen and Johnson, 2001]:…”
Section: Discussionmentioning
confidence: 99%
“…On the other hand, the Lie group method is an effective method for studying conservation laws, performing Lie symmetry analysis, and finding exact solutions to nonlinear partial differential equations. In some recent findings, the symmetric analysis of spherical and cylindrical KdV has been discussed in detail [19,20]. For our purpose, we have applied a standard reductive perturbation technique and obtained the Korteweg-De Vries (KdV) equation, which admits the excitation of phase-shaped solitons.…”
Section: Introductionmentioning
confidence: 99%