(Non)linear instability of periodic traveling waves: Klein–Gordon and KdV type equations

• Main Authors: Angulo Pava Jaime, Natali Fabio
• Format: Article
• Language: English
• Published: De Gruyter 2014-05-01
• Series: Advances in Nonlinear Analysis
• Subjects: linear stability; (non)linear instability; critical klein–gordon equation; critical kdv; kdv type models; 35q51; 35b35; 35b10; 35c07
• Online Access: https://doi.org/10.1515/anona-2014-0008
• ISSN: 2191-9496; 2191-950X

We prove the existence and nonlinear instability of periodic traveling wave solutions for the critical one-dimensional Klein–Gordon equation. We also establish a linear instability criterium for a KdV type system. An application of this approach is made to obtain the linear/nonlinear instability of vector cnoidal wave profiles. Finally, via a theoretical and numerical approach we show the linear stability or instability of periodic positive and sign changing waves, respectively, for the critical Korteweg–de Vries equation.