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

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abstract

  • Abstract. 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.

publication date

  • May 1, 2014