TY - JOUR
T1 - Modulational instability in equations of KdV type
AU - Bronski, Jared C.
AU - Hur, Vera Mikyoung
AU - Johnson, Mathew A.
N1 - JCB is supported by the National Science Foundation grant DMS-1211364. VMH is supported by the National Science Foundation grant CAREER DMS-1352597 and an Alfred P. Sloan Foundation Fellowship. MAJ is supported by the National Science Foundation grant DMS-1211183.
PY - 2016
Y1 - 2016
N2 - It is a matter of experience that nonlinear waves in a dispersive medium, propagating primarily in one direction, may appear periodic in small space and time scales, but their characteristics—the amplitude, the phase, the wave number, etc.—slowly vary in large space and time scales. In the 1960s, Whitham developed an asymptotic (WKB) method to study the effects of small “modulations” on nonlinear dispersive waves. Since then, there has been a great deal of work aiming at rigorously justifying the predictions from Whitham’s formal theory. We discuss some recent advances in the mathematical understanding of the dynamics, in particular, the instability, of slowly modulated waves for equations of KdV type.
AB - It is a matter of experience that nonlinear waves in a dispersive medium, propagating primarily in one direction, may appear periodic in small space and time scales, but their characteristics—the amplitude, the phase, the wave number, etc.—slowly vary in large space and time scales. In the 1960s, Whitham developed an asymptotic (WKB) method to study the effects of small “modulations” on nonlinear dispersive waves. Since then, there has been a great deal of work aiming at rigorously justifying the predictions from Whitham’s formal theory. We discuss some recent advances in the mathematical understanding of the dynamics, in particular, the instability, of slowly modulated waves for equations of KdV type.
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U2 - 10.1007/978-3-319-20690-5_4
DO - 10.1007/978-3-319-20690-5_4
M3 - Article
AN - SCOPUS:84939857080
SN - 0075-8450
VL - 908
SP - 83
EP - 133
JO - Lecture Notes in Physics
JF - Lecture Notes in Physics
ER -