Abstract
In this paper we prove the existence of hylomorphic solitons in the generalized KdV equation. Following (Benci, Milan J Math 77:271–332, 2009), a soliton is called hylomorphic if it is a solitary wave whose stability is due to a particular relation between energy and another integral of motion which we call hylenic charge.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bellazzini, J., Benci, V., Ghimenti, M., Micheletti, A.M.: On the existence of the fundamental eigenvalue of an elliptic problem in \(\mathbb{R}^{N}\). Adv. Nonlinear Stud. 7(3), 439–458 (2007)
Benci, V.: Hylomorphic solitons. Milan J. Math. 77, 271–332 (2009)
Benci, V., Fortunato, D.: A minimization method and applications to the study of solitons. Nonlinear Anal. 75(12), 4398–4421 (2012)
Benci, V., Fortunato, D.: Solitons in Schrödinger-Maxwell equations. J. Fixed Point Theory Appl. 15(1), 101–132 (2014)
Benci, V., Donato Fortunato, D.: Variational methods in nonlinear field equations. Solitary waves, hylomorphic solitons and vortices. Springer Monographs in Mathematics. Springer, Cham (2014)
Cazenave, T., Lions, P.-L.: Orbital stability of standing waves for some nonlinear Schrödinger equations. Commun. Math. Phys. 85(4), 549–561 (1982)
Kato, T.: On the Cauchy problem for the (generalized) Korteweg-de Vries equation. In: Studies in applied mathematics. Advance Mathematical Supplement Stud. vol. 8, pp. 93–128. Academic Press, New York (1983)
Kenig, C.E., Ponce, G., Vega, L.: Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle. Commun. Pure Appl. Math. 46(4), 527–620 (1993)
Sulem, C., Sulem, P.-L.: The Nonlinear Schrödinger Equation. Self-focusing and Wave Collapse. Applied Mathematical Sciences, vol. 139. Springer, New York (1999)
Tsutsumi, M., Mukasa, T., Riichi Iino, R.: On the generalized Korteweg-de Vries equation. Proc. Jpn. Acad. 46, 921–925 (1970)
Weinstein, M.I.: Lyapunov stability of ground states of nonlinear dispersive evolution equations. Commun. Pure Appl. Math. 39(1), 51–67 (1986)
Whitham, G.B.: Linear and Nonlinear Waves. Pure and Applied Mathematics. Wiley, New York (1974)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Additional information
Dedicated to our friend Djairo De Figuereido on the occasion of his 80th birthday
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Benci, V., Fortunato, D. (2015). Hylomorphic solitons for the generalized KdV equation. In: Nolasco de Carvalho, A., Ruf, B., Moreira dos Santos, E., Gossez, JP., Monari Soares, S., Cazenave, T. (eds) Contributions to Nonlinear Elliptic Equations and Systems. Progress in Nonlinear Differential Equations and Their Applications, vol 86. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-19902-3_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-19902-3_2
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-19901-6
Online ISBN: 978-3-319-19902-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)