Stability of multipeakons
Khaled El Dika, Luc Molinet (2009)
Annales de l'I.H.P. Analyse non linéaire
Kalisch, Henrik, Nguyen, Nguyet Thanh (2009)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Lopes, Orlando (2003)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Sylvie Benzoni-Gavage, Pascal Noble, L. Miguel Rodrigues (2013)
Journées Équations aux dérivées partielles
Partial differential equations endowed with a Hamiltonian structure, like the Korteweg–de Vries equation and many other more or less classical models, are known to admit rich families of periodic travelling waves. The stability theory for these waves is still in its infancy though. The issue has been tackled by various means. Of course, it is always possible to address stability from the spectral point of view. However, the link with nonlinear stability - in fact, orbital stability, since we are...
Carlos F. Vasconcellos, Patricia N. da Silva (2011)
ESAIM: Control, Optimisation and Calculus of Variations
We study the stabilization of global solutions of the Kawahara (K) equation in a bounded interval, under the effect of a localized damping mechanism. The Kawahara equation is a model for small amplitude long waves. Using multiplier techniques and compactness arguments we prove the exponential decay of the solutions of the (K) model. The proof requires of a unique continuation theorem and the smoothing effect of the (K) equation on the real line, which are proved in this work.
Carlos F. Vasconcellos, Patricia N. da Silva (2011)
ESAIM: Control, Optimisation and Calculus of Variations
We study the stabilization of global solutions of the Kawahara (K) equation in a bounded interval, under the effect of a localized damping mechanism. The Kawahara equation is a model for small amplitude long waves. Using multiplier techniques and compactness arguments we prove the exponential decay of the solutions of the (K) model. The proof requires of a unique continuation theorem and the smoothing effect of the (K) equation on the real line, which are proved in this work.
Zhu, Jianmin, Li, Zhixiang, Liu, Yicheng (2006)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Kiselev, Arthemy V., Wolf, Thomas (2006)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Schmidtt, David M. (2010)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Boris A. Rosenfeld, Nadezhda E. Maryukova (1997)
Publications de l'Institut Mathématique
Bracken, Paul (2005)
International Journal of Mathematics and Mathematical Sciences
Gama, Silvio Marques A., Smirnov, Gueorgui (2009)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Adomian, G. (1996)
International Journal of Mathematics and Mathematical Sciences
Babujian, Hratchya M., Foerster, Angela, Karowski, Michael (2006)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Rashid, Abdur, Ismail, Ahmad Izani Bin Md. (2009)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
Smaoui, Nejib, Mekkaoui, Mona (2004)
Journal of Applied Mathematics and Stochastic Analysis
Yi Wei, Xin-Dang He, Xiao-Feng Yang (2016)
Open Mathematics
The homogeneous balance of undetermined coefficients method is firstly proposed to solve such nonlinear partial differential equations (PDEs), the balance numbers of which are not positive integers. The proposed method can also be used to derive more general bilinear equation of nonlinear PDEs. The Eckhaus equation, the KdV equation and the generalized Boussinesq equation are chosen to illustrate the validity of our method. The proposed method is also a standard and computable method, which can...
Björn Birnir, Gustavo Ponce, Nils Svanstedt (1996)
Annales de l'I.H.P. Analyse non linéaire
A.I. Bobenko, Sergej B. Kuksin (1995)
Commentarii mathematici Helvetici
Mironov, A.E. (2004)
Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]