An exactly solvable problem of wave fronts and applications to the asymptotic theory Yu. V. Brezhnev, A. V. Tsvetkova
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ArticleContent type: Текст Media type: электронный Subject(s): гамильтоновы системы | волновые фронты | асимптотическая теория | эллиптические функцииGenre/Form: статьи в журналах Online resources: Click here to access online
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Physica D: Nonlinear Phenomena Vol. 419. P. 132868 (1-8)Abstract: A nontrivially solvable 4-dimensional Hamiltonian system is applied to the problem of wave fronts and to the asymptotic theory of partial differential equations. The Hamilton function we consider is . Such Hamiltonians arise when describing the fronts of linear waves generated by a localized source in a basin with a variable depth. We consider two realistic types of bottom shape: 1) the depth of the basin is determined, in the polar coordinates, by the function and 2) the depth function is . As an application, we construct the asymptotic solution to the wave equation with localized initial conditions and asymptotic solutions of the Helmholtz equation with a localized right-hand side.
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A nontrivially solvable 4-dimensional Hamiltonian system is applied to the problem of wave fronts and to the asymptotic theory of partial differential equations. The Hamilton function we consider is . Such Hamiltonians arise when describing the fronts of linear waves generated by a localized source in a basin with a variable depth. We consider two realistic types of bottom shape: 1) the depth of the basin is determined, in the polar coordinates, by the function and 2) the depth function is . As an application, we construct the asymptotic solution to the wave equation with localized initial conditions and asymptotic solutions of the Helmholtz equation with a localized right-hand side.
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