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math.AP2019
Stability of periodic waves for the fractional KdV and NLS equations
Sevdzhan Hakkaev, Atanas G. Stefanov
We consider the focusing fractional periodic Korteweg-deVries (fKdV) and fractional periodic nonlinear Schrödinger equations (fNLS) equations, with sub-critical dispersion. I…
math.AP2019
Sharp relaxation rates for plane waves of reaction-diffusion systems
Fazel Hadadifard, Atanas G. Stefanov
It is well-known and classical result that spectrally stable traveling waves of a general reaction-diffusion system in one spatial dimension are asymptotically stable with exponent…