RUSA Lec.63-The Hirota Bilinear Method and Fermi Pasta Ulam Tsingou Recurrence-Prof. K. W. Chow скачать в хорошем качестве

RUSA Lec.63-The Hirota Bilinear Method and Fermi Pasta Ulam Tsingou Recurrence-Prof. K. W. Chow

TITLE: The Hirota Bilinear Method, Solitons, Rogue Waves and Fermi-Pasta-Ulam-Tsingou Recurrence ABSTRACT: ‘Solitons’ are propagating, localized modes arising from a balance between dispersion and nonlinearity. Intensive studies since the 1960s have generated ingenious theoretical techniques as well as many applications to physical disciplines, e.g. fluid mechanics, optics and plasma. The Hirota bilinear method for solving the ‘multi-soliton’ of ‘integrable’ nonlinear equations is discussed. In particular, a singular long wave limit can lead to rational exact solutions and rogue wave modes. Rogue waves are unexpectedly large displacements from an otherwise tranquil background. The Hirota method can also be applied under periodic boundary conditions by utilizing elliptic and theta functions. The connections among rogue waves, breather modes, and the classical problem of Fermi-Pasta-Ulam-Tsingou recurrence are assessed. Such recurrence is indeed observed in experiments in fluid mechanics and optics.