منابع مشابه
Wave breaking in the short-pulse equation
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 short-pulse equation and holds both on an infinite line and in a periodic domain. Numerical illustrations of the finite-time wave breaking are given in a periodic ...
متن کاملSolitary Wave Solutions of the Short Pulse Equation
An exact nonsingular solitary wave solution of the Schäfer–Wayne short pulse equation is derived from the breather solution of the sine-Gordon equation by means of a transformation between these two integrable equations. The short pulse equation (SPE), which has the form uxt = u+ 1 6 ( u ) xx (1) up to scale transformations of its variables, was derived by Schäfer and Wayne [1] as a model equat...
متن کاملWave Breaking in the Ostrovsky-Hunter Equation
The Ostrovsky–Hunter equation governs evolution of shallow water waves on a rotating fluid in the limit of small high-frequency dispersion. Sufficient conditions for the wave breaking in the Ostrovsky–Hunter equation are found both on an infinite line and in a periodic domain. Using the method of characteristics, we also specify the blow-up rate at which the waves break. Numerical illustrations...
متن کاملRigorous justification of the short-pulse equation
We prove that the short-pulse equation, which is derived from a quasilinear Klein–Gordon equation with formal asymptotic methods, can be rigorously justified. The justification procedure applies to small-norm solutions of the short-pulse equation. Although the small-norm solutions exist for infinite times and include modulated pulses and their elastic interactions, the error bound for arbitrary...
متن کاملGeneralizations of the short pulse equation
We classify integrable scalar polynomial partial differential equations of second order generalizing the short pulse equation.
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ژورنال
عنوان ژورنال: Dynamics of Partial Differential Equations
سال: 2009
ISSN: 1548-159X,2163-7873
DOI: 10.4310/dpde.2009.v6.n4.a1