相关论文: Wave breaking in the Ostrovsky--Hunter equation

The Ostrovsky-Hunter equation provides a model for small-amplitude long waves in a rotating fluid of finite depth. It is a nonlinear evolution equation. In this paper we study the well-posedness for the Cauchy problem associated to this…

The Ostrovsky-Hunter equation provides a model for small-amplitude long waves in a rotating fluid of finite depth. It is a nonlinear evolution equation. In this paper we study the well-posedness for the Cauchy problem associated to this…

The Ostrovsky-Hunter equation provides a model for small-amplitude long waves in a rotating fluid of finite depth. It is a nonlinear evolution equation. In this paper the welposed- ness of bounded solutions for a non-homogeneous initial…

Sufficient conditions for wave breaking are found for the short-pulse equation describing wave packets of few cycles on the ultra-short pulse scale. The analysis relies on the method of characteristics and conserved quantities of the…

A family of Camassa-Holm type equations with a linear term and cubic and quartic nonlinearities is considered. Local well-posedness results are established via Kato's approach. Conserved quantities for the equation are determined and from…

We study the periodic Ostrovsky-Hunter equation in the case where the flux function may depend on the spatial variable. Our main results are that if the flux function is twice differentiable, then there exists a unique entropy solution.…

Ostrovsky's equation with time- and space- dependent forcing is studied. This equation is model for long waves in a rotating fluid with a non-constant depth (topography). A classification of Lie point symmetries and low-order conservation…

Based on recent well-posedness results in Sobolev (or Besov spaces) for periodic solutions to the Fornberg-Whitham equations we investigate here the questions of wave breaking and blow-up for these solutions. We show first that finite…

We prove wave breaking --- bounded solutions with unbounded derivatives --- in the nonlinear nonlocal equations which combine the dispersion relation of water waves and the nonlinear shallow water equations, and which generalize the Whitham…

The problem of wave breaking during its propagation in the Bose-Einstein condensate to a stationary medium is considered for the case when the initial profile at the breaking instant can be approximated by a power function of the form…

We prove wave breaking --- bounded solutions with unbounded derivatives --- in the nonlinear nonlocal equation which combines the dispersion relation of water waves and a nonlinearity of the shallow water equations, provided that the slope…

Periodic and solitary travelling-wave solutions of an extended reduced Ostrovsky equation are investigated. Attention is restricted to solutions that, for the appropriate choice of certain constant parameters, reduce to solutions of the…

We modify the nonlinear shallow water equations, the Korteweg-de Vries equation, and the Whitham equation, to permit constant vorticity, and examine wave breaking, or the lack thereof. By wave breaking, we mean that the solution remains…

We show wave breaking for the Whitham equation in a range of fractional dispersion, i.e. the solution remains bounded but its slope becomes unbounded in finite time, provided that the initial datum is sufficiently steep.

Following conservative solutions of the nonlinear variational wave equation $u_{tt}-c(u)(c(u)u_x)_x=0$ along forward and backward characteristics, we identify criteria, which guarantee that wave breaking either occurs in the nearby future…

Periodic travelling waves are considered in the class of reduced Ostrovsky equations that describe low-frequency internal waves in the presence of rotation. The reduced Ostrovsky equations with either quadratic or cubic nonlinearities can…

Considered herein is the initial-value problem for the generalized periodic Camassa-Holm equation which is related to the Camassa-Holm equation and the Hunter-Saxton equation. Sufficient conditions guaranteeing the development of breaking…

We consider the Ostrovsky-Hunter type equation that includes the short pulse. We con- sider here the asymptotic behavior as gamma goes to 0. The proof relies on deriving suitable a priori estimates together with an application of the…

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…

We consider the Ostrovsky equation, which contains nonlinear dispersive effects. We prove that as the diffusion parameter tend to zero, the solutions of the dispersive equation converge to discontinuous weak solutions of the…