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math.AP2009★ 27 cited
An index theorem for the stability of periodic traveling waves of KdV type
Jared C. Bronski, Mathew A. Johnson, Todd Kapitula
We consider periodic solutions to equations of Korteweg-Devries type. While the stability theory for periodic waves has received much some attention the theory is much less develop…
math.AP2009
The Transverse Instability of Periodic Waves in Zakharov-Kuznetsov Type Equations
Mathew A. Johnson
In this paper, we investigate the instability of one-dimensionally stable periodic traveling wave solutions of the generalized Korteweg-de Vries equation to long wavelength transve…
math.AP2009★ 1 cited
Nonlinear Stability of Periodic Traveling Wave Solutions of the Generalized Korteweg-de Vries Equation
Mathew A. Johnson
In this paper, we study the orbital stability for a four-parameter family of periodic stationary traveling wave solutions to the generalized Korteweg-de Vries equation. In particul…