A Linear Liouville Property for the Generalized Kawahara Equation
Résumé
In Kabakouala and Molinet [6], we construct a family of smooth-even solitons by applying the Implicit Function Theorem in the neighborhood of the explicit soliton of the generalized Kawahara equation (gKW), found by Dey et al [5]. Next, by combining the well-known spectral method introduced by Benjamin [3] with the continuity arguments, we proved the orbital stability of these family for the subcritical and critical generalized Korteweg-de Vries equation (gKdV) nonlinearity power. In this paper, inspired by the Martel's Method [8] on the gKdV equation, we prove that the solution of the linearized gKW equation around these family of solitons which is uniformly localized becomes static (independent of time), and coincides to the first derivative of the soliton.
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