منابع مشابه
On a Whitham-type Equation
The Hunter–Saxton equation and the Gurevich–Zybin system are considered as two mutually non-equivalent representations of one and the same Whitham-type equation, and all their common solutions are obtained exactly.
متن کاملTraveling Waves for the Whitham Equation
The existence of traveling waves for the original Whitham equation is investigated. This equation combines a generic nonlinear quadratic term with the exact linear dispersion relation of surface water waves of finite depth. It is found that there exist small-amplitude periodic traveling waves with sub-critical speeds. As the period of these traveling waves tends to infinity, their velocities ap...
متن کاملGlobal Bifurcation for the Whitham Equation
We prove the existence of a global bifurcation branch of 2π-periodic, smooth, traveling-wave solutions of the Whitham equation. It is shown that any subset of solutions in the global branch contains a sequence which converges uniformly to some solution of Hölder class C, α < 1 2 . Bifurcation formulas are given, as well as some properties along the global bifurcation branch. In addition, a spec...
متن کاملA type of bounded traveling wave solutions for the Fornberg-Whitham equation
In this paper, by using bifurcation method, we successfully find the FornbergWhitham equation ut − uxxt + ux = uuxxx − uux + 3uxuxx, has a type of traveling wave solutions called kink-like wave solutions and antikinklike wave solutions. They are defined on some semifinal bounded domains and possess properties of kink waves and anti-kink waves. Their implicit expressions are obtained. For some c...
متن کاملOn Hilbert Golab-Schinzel type functional equation
Let $X$ be a vector space over a field $K$ of real or complex numbers. We will prove the superstability of the following Go{l}c{a}b-Schinzel type equation$$f(x+g(x)y)=f(x)f(y), x,yin X,$$where $f,g:Xrightarrow K$ are unknown functions (satisfying some assumptions). Then we generalize the superstability result for this equation with values in the field of complex numbers to the case of an arbitr...
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ژورنال
عنوان ژورنال: Symmetry, Integrability and Geometry: Methods and Applications
سال: 2009
ISSN: 1815-0659
DOI: 10.3842/sigma.2009.101