On the Existence and Conditional Energetic Stability of Solitary GravityCapillary Surface Waves on Deep Water
(2011) In Journal of Mathematical Fluid Mechanics 13(4). p.593627 Abstract
 This paper presents an existence and stability theory for gravitycapillary solitary waves on the surface of a body of water of infinite depth. Exploiting a classical variational principle, we prove the existence of a minimiser of the wave energy epsilon subject to the constraint I = root 2 mu, where I is the wave momentum and 0 < mu << 1. Since epsilon and I are both conserved quantities a standard argument asserts the stability of the set Dmu of minimisers: solutions starting near Dmu remain close to Dmu in a suitably defined energy space over their interval of existence. In the applied mathematics literature solitary water waves of the present kind are modelled as solutions of the nonlinear Schrodinger equation with cubic... (More)
 This paper presents an existence and stability theory for gravitycapillary solitary waves on the surface of a body of water of infinite depth. Exploiting a classical variational principle, we prove the existence of a minimiser of the wave energy epsilon subject to the constraint I = root 2 mu, where I is the wave momentum and 0 < mu << 1. Since epsilon and I are both conserved quantities a standard argument asserts the stability of the set Dmu of minimisers: solutions starting near Dmu remain close to Dmu in a suitably defined energy space over their interval of existence. In the applied mathematics literature solitary water waves of the present kind are modelled as solutions of the nonlinear Schrodinger equation with cubic focussing nonlinearity. We show that the waves detected by our variational method converge (after an appropriate rescaling) to solutions of this model equation as mu down arrow 0. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/2377716
 author
 Groves, M. D. and Wahlén, Erik ^{LU}
 organization
 publishing date
 2011
 type
 Contribution to journal
 publication status
 published
 subject
 in
 Journal of Mathematical Fluid Mechanics
 volume
 13
 issue
 4
 pages
 593  627
 publisher
 Birkhaüser
 external identifiers

 wos:000300352500007
 scopus:80855165477
 ISSN
 14226928
 DOI
 10.1007/s000210100034x
 language
 English
 LU publication?
 yes
 id
 1849dc9d805640d1b433e7f3de6d851c (old id 2377716)
 date added to LUP
 20120327 12:04:47
 date last changed
 20180114 03:37:51
@article{1849dc9d805640d1b433e7f3de6d851c, abstract = {This paper presents an existence and stability theory for gravitycapillary solitary waves on the surface of a body of water of infinite depth. Exploiting a classical variational principle, we prove the existence of a minimiser of the wave energy epsilon subject to the constraint I = root 2 mu, where I is the wave momentum and 0 < mu << 1. Since epsilon and I are both conserved quantities a standard argument asserts the stability of the set Dmu of minimisers: solutions starting near Dmu remain close to Dmu in a suitably defined energy space over their interval of existence. In the applied mathematics literature solitary water waves of the present kind are modelled as solutions of the nonlinear Schrodinger equation with cubic focussing nonlinearity. We show that the waves detected by our variational method converge (after an appropriate rescaling) to solutions of this model equation as mu down arrow 0.}, author = {Groves, M. D. and Wahlén, Erik}, issn = {14226928}, language = {eng}, number = {4}, pages = {593627}, publisher = {Birkhaüser}, series = {Journal of Mathematical Fluid Mechanics}, title = {On the Existence and Conditional Energetic Stability of Solitary GravityCapillary Surface Waves on Deep Water}, url = {http://dx.doi.org/10.1007/s000210100034x}, volume = {13}, year = {2011}, }