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On the ground states of the Ostrovskyi equation and their stability
Author(s) -
Posukhovskyi Iurii,
Stefanov Atanas
Publication year - 2020
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12309
Subject(s) - compact space , amplitude , hamiltonian (control theory) , mathematics , mathematical analysis , norm (philosophy) , ordinary differential equation , fourier transform , stability (learning theory) , pulse (music) , physics , classical mechanics , mathematical physics , differential equation , quantum mechanics , mathematical optimization , machine learning , political science , computer science , law , voltage
The Ostrovskyi (Ostrovskyi‐Vakhnenko/short pulse) equations are ubiquitous models in mathematical physics. They describe water waves under the action of a Coriolis force as well as the amplitude of a “short” pulse in an optical fiber. In this paper, we rigorously construct ground traveling waves for these models as minimizers of the Hamiltonian functional for any fixed L 2 norm. The existence argument proceeds via the method of compensated compactness, but it requires surprisingly detailed Fourier analysis arguments to rule out the nonvanishing of the limits of the minimizing sequences. We show that all of these waves are weakly nondegenerate and spectrally stable.