# American Institute of Mathematical Sciences

January  2002, 8(1): 115-119. doi: 10.3934/dcds.2002.8.115

## A linearized instability result for solitary waves

 1 Departamento de Matematica - IMECC, UNICAMP, C.P. 6065, Campinas, SP, Brazil

Received  March 2001 Revised  June 2001 Published  October 2001

In this paper we prove an abstract instability result for the linearized hamiltonian

$\dot u = JEu$

in a Hilbert space $X$ without assuming that $J$ is onto.

Citation: Orlando Lopes. A linearized instability result for solitary waves. Discrete & Continuous Dynamical Systems - A, 2002, 8 (1) : 115-119. doi: 10.3934/dcds.2002.8.115
 [1] José Raúl Quintero, Juan Carlos Muñoz Grajales. Solitary waves for an internal wave model. Discrete & Continuous Dynamical Systems - A, 2016, 36 (10) : 5721-5741. doi: 10.3934/dcds.2016051 [2] Jerry Bona, Hongqiu Chen. Solitary waves in nonlinear dispersive systems. Discrete & Continuous Dynamical Systems - B, 2002, 2 (3) : 313-378. doi: 10.3934/dcdsb.2002.2.313 [3] Emmanuel Hebey. Solitary waves in critical Abelian gauge theories. Discrete & Continuous Dynamical Systems - A, 2012, 32 (5) : 1747-1761. doi: 10.3934/dcds.2012.32.1747 [4] Yiren Chen, Zhengrong Liu. The bifurcations of solitary and kink waves described by the Gardner equation. Discrete & Continuous Dynamical Systems - S, 2016, 9 (6) : 1629-1645. doi: 10.3934/dcdss.2016067 [5] H. Kalisch. Stability of solitary waves for a nonlinearly dispersive equation. Discrete & Continuous Dynamical Systems - A, 2004, 10 (3) : 709-717. doi: 10.3934/dcds.2004.10.709 [6] John Boyd. Strongly nonlinear perturbation theory for solitary waves and bions. Evolution Equations & Control Theory, 2019, 8 (1) : 1-29. doi: 10.3934/eect.2019001 [7] David Henry, Hung-Chu Hsu. Instability of equatorial water waves in the $f-$plane. Discrete & Continuous Dynamical Systems - A, 2015, 35 (3) : 909-916. doi: 10.3934/dcds.2015.35.909 [8] Jifeng Chu, Delia Ionescu-Kruse, Yanjuan Yang. Exact solution and instability for geophysical waves at arbitrary latitude. Discrete & Continuous Dynamical Systems - A, 2019, 39 (8) : 4399-4414. doi: 10.3934/dcds.2019178 [9] Juan Belmonte-Beitia, Vladyslav Prytula. Existence of solitary waves in nonlinear equations of Schrödinger type. Discrete & Continuous Dynamical Systems - S, 2011, 4 (5) : 1007-1017. doi: 10.3934/dcdss.2011.4.1007 [10] Hung-Chu Hsu. Recovering surface profiles of solitary waves on a uniform stream from pressure measurements. Discrete & Continuous Dynamical Systems - A, 2014, 34 (8) : 3035-3043. doi: 10.3934/dcds.2014.34.3035 [11] Philippe Gravejat. Asymptotics of the solitary waves for the generalized Kadomtsev-Petviashvili equations. Discrete & Continuous Dynamical Systems - A, 2008, 21 (3) : 835-882. doi: 10.3934/dcds.2008.21.835 [12] David Usero. Dark solitary waves in nonlocal nonlinear Schrödinger systems. Discrete & Continuous Dynamical Systems - S, 2011, 4 (5) : 1327-1340. doi: 10.3934/dcdss.2011.4.1327 [13] Santosh Bhattarai. Stability of normalized solitary waves for three coupled nonlinear Schrödinger equations. Discrete & Continuous Dynamical Systems - A, 2016, 36 (4) : 1789-1811. doi: 10.3934/dcds.2016.36.1789 [14] Amin Esfahani, Steve Levandosky. Solitary waves of the rotation-generalized Benjamin-Ono equation. Discrete & Continuous Dynamical Systems - A, 2013, 33 (2) : 663-700. doi: 10.3934/dcds.2013.33.663 [15] Andrew Comech, David Stuart. Small amplitude solitary waves in the Dirac-Maxwell system. Communications on Pure & Applied Analysis, 2018, 17 (4) : 1349-1370. doi: 10.3934/cpaa.2018066 [16] Kristoffer Varholm. Solitary gravity-capillary water waves with point vortices. Discrete & Continuous Dynamical Systems - A, 2016, 36 (7) : 3927-3959. doi: 10.3934/dcds.2016.36.3927 [17] Steve Levandosky, Yue Liu. Stability and weak rotation limit of solitary waves of the Ostrovsky equation. Discrete & Continuous Dynamical Systems - B, 2007, 7 (4) : 793-806. doi: 10.3934/dcdsb.2007.7.793 [18] Amjad Khan, Dmitry E. Pelinovsky. Long-time stability of small FPU solitary waves. Discrete & Continuous Dynamical Systems - A, 2017, 37 (4) : 2065-2075. doi: 10.3934/dcds.2017088 [19] Daniele Cassani, João Marcos do Ó, Abbas Moameni. Existence and concentration of solitary waves for a class of quasilinear Schrödinger equations. Communications on Pure & Applied Analysis, 2010, 9 (2) : 281-306. doi: 10.3934/cpaa.2010.9.281 [20] Cheng Hou Tsang, Boris A. Malomed, Kwok Wing Chow. Exact solutions for periodic and solitary matter waves in nonlinear lattices. Discrete & Continuous Dynamical Systems - S, 2011, 4 (5) : 1299-1325. doi: 10.3934/dcdss.2011.4.1299

2018 Impact Factor: 1.143