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Geyer, A. (author), Quirchmayr, Ronald (author)We develop a KortewegDe Vries (KdV) theory for weakly nonlinear waves in discontinuously stratified twolayer fluids with a generally prescribed rotational steady current. With the help of a classical asymptotic power series approach, these models are directly derived from the divergencefree incompressible Euler equations for unidirectional...journal article 2022
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Gasull, Armengol (author), Geyer, A. (author), Mañosa, Víctor (author)It is well known that the existence of traveling wave solutions (TWS) for many partial differential equations (PDE) is a consequence of the fact that an associated planar ordinary differential equation (ODE) has certain types of solutions defined for all time. In this paper we address the problem of persistence of TWS of a given PDE under small...journal article 2021
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Geyer, A. (author), Martins, Renan H. (author), Natali, Fábio (author), Pelinovsky, Dmitry E. (author)We solve the open problem of spectral stability of smooth periodic waves in the Camassa–Holm equation. The key to obtaining this result is that the periodic waves of the Camassa–Holm equation can be characterized by an alternative Hamiltonian structure, different from the standard formulation common to the Kortewegde Vries equation. The...journal article 2021
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Gasull, A. (author), Geyer, A. (author), Mañosas, F. (author)We show that a family of certain definite integrals forms a Chebyshev system if two families of associated functions appearing in their integrands are Chebyshev systems as well. We apply this criterion to several examples which appear in the context of perturbations of periodic nonautonomous ODEs to determine bounds on the number of isolated...journal article 2020
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Geyer, A. (author), Pelinovsky, Dmitry E. (author)We show that the peaked periodic traveling wave of the reduced Ostrovsky equations with quadratic and cubic nonlinearity is spectrally unstable in the space of square integrable periodic functions with zero mean and the same period. We discover that the spectrum of a linearized operator at the peaked periodic wave completely covers a closed...journal article 2020
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Geyer, A. (author), Quirchmayr, Ronald (author)Motivated by the question whether higherorder nonlinear model equations, which go beyond the CamassaHolm regime of moderate amplitude waves, could point us to new types of waves profiles, we study the traveling wave solutions of a quasilinear evolution equation which models the propagation of shallow water waves of large amplitude. The aim of...journal article 2018
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Geyer, A. (author), Quirchmayr, Ronald (author)We present derivations of shallow water model equations of Korteweg–de Vries and Boussinesq type for equatorial tsunami waves in the fplane approximation and discuss their applicability.journal article 2018
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Bruell, G. (author), Ehrnström, Mats (author), Geyer, A. (author), Pei, Long (author)We show that for a large class of evolutionary nonlinear and nonlocal partial differential equations, symmetry of solutions implies very restrictive properties of the solutions and symmetry axes. These restrictions are formulated in terms of three principles, based on the structure of the equations. The first principle covers equations that...journal article 2017
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Geyer, A. (author), Pelinovsky, Dmitry (author)We consider stability of periodic travelling waves in the generalized reduced Ostrovsky equation with respect to coperiodic perturbations. Compared to the recent literature, we give a simple argument that proves spectral stability of all smooth periodic travelling waves independent of the nonlinearity power. The argument is based on the...journal article 2017