Analytical and numerical methods for the CMKdV-II equation.
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Akin, Ömer, Özuğurlu, Ersin (2009)
Mathematical Problems in Engineering
Zedan, Hassan (2010)
Boundary Value Problems [electronic only]
Yvan Martel, Frank Merle, Pierre Raphaël (2011/2012)
Séminaire Laurent Schwartz — EDP et applications
These notes present the main results of [22, 23, 24] concerning the mass critical (gKdV) equation for initial data in close to the soliton. These works revisit the blow up phenomenon close to the family of solitons in several directions: definition of the stable blow up and classification of all possible behaviors in a suitable functional setting, description of the minimal mass blow up in , construction of various exotic blow up rates in , including grow up in infinite time.
Yvan Martel, Frank Merle, Pierre Raphaël (2015)
Journal of the European Mathematical Society
We consider the mass critical (gKdV) equation for initial data in . We first prove the existence and uniqueness in the energy space of a minimal mass blow up solution and give a sharp description of the corresponding blow up soliton-like bubble. We then show that this solution is the universal attractor of all solutions near the ground state which have a defocusing behavior. This allows us to sharpen the description of near soliton dynamics obtained in [29].
Raphaël Côte (2006/2007)
Séminaire Équations aux dérivées partielles
Peng, Yan-Ze (2009)
International Journal of Mathematics and Mathematical Sciences
Gómez S, Cesar A., Salas, Alvaro H., Frias, Bernardo Acevedo (2010)
Mathematical Problems in Engineering
Claudio Muñoz (2011/2012)
Séminaire Laurent Schwartz — EDP et applications
The aim of this note is to give a short review of our recent work (see [5]) with Miguel A. Alejo and Luis Vega, concerning the -stability, and asymptotic stability, of the -soliton of the Korteweg-de Vries (KdV) equation.
Song, Ming, Li, Shaoyong, Cao, Jun (2010)
Abstract and Applied Analysis
Borhanifar, A., Jafari, H., Karim, S.A. (2008)
The Journal of Nonlinear Sciences and its Applications
Caliari, Marco, Squassina, Marco (2010)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Haci Mehmet Baskonus, Hasan Bulut (2015)
Open Mathematics
In this paper, we apply the Fractional Adams-Bashforth-Moulton Method for obtaining the numerical solutions of some linear and nonlinear fractional ordinary differential equations. Then, we construct a table including numerical results for both fractional differential equations. Then, we draw two dimensional surfaces of numerical solutions and analytical solutions by considering the suitable values of parameters. Finally, we use the L2 nodal norm and L∞ maximum nodal norm to evaluate the accuracy...
Visinescu, Anca, Grecu, Dan, Fedele, Renato, De Nicola, Sergio (2011)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Zhou, Jiangbo, Tian, Lixin (2009)
Mathematical Problems in Engineering
Varlamov, Vladimir (2010)
International Journal of Differential Equations
Shateri, Majid, Ganji, D.D. (2010)
International Journal of Differential Equations
Panayotaros, Panayotis, Sepulveda, Mauricio, Vera, Octavio (2010)
Electronic Journal of Differential Equations (EJDE) [electronic only]
De Bouard, Anne, Debussche, Arnaud (2009)
Electronic Journal of Probability [electronic only]
K. Kirkpatrick (2012)
Mathematical Modelling of Natural Phenomena
We review some recent results concerning Gibbs measures for nonlinear Schrödinger equations (NLS), with implications for the theory of the NLS, including stability and typicality of solitary wave structures. In particular, we discuss the Gibbs measures of the discrete NLS in three dimensions, where there is a striking phase transition to soliton-like behavior.
André de Laire, Philippe Gravejat (2014/2015)
Séminaire Laurent Schwartz — EDP et applications
Cet exposé présente plusieurs résultats récents quant à la stabilité des solitons sombres de l’équation de Landau-Lifshitz à anisotropie planaire, en particulier, quant à la stabilité orbitale des trains (bien préparés) de solitons gris [16] et à la stabilité asymptotique de ces mêmes solitons [2].
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