The Newell-whitehead-segel Equation for Traveling Waves
نویسنده
چکیده
An equation to describe nearly 1D traveling-waves patterns is put forward in the form of a dispersive generalization of the Newell-Whitehead-Segel equation. Transverse stability of plane waves is shown to be drastically altered by the dispersion. A necessary transverse Benjamin-Feir stability condition is obtained. If it is met, a quarter of the plane-wave existence band is unstable, while three quarters are transversely stable. Next, linear defects in the form of grain boundaries (GB’s) are studied. An effective Burgers equation is derived, in the framework of which a GB is tantamount to a shock wave. Asymmetric GB’s are moving at a constant velocity. PACS numbers (“American”): 47.27.Te; 47.52.+j; 03.40.Kf
منابع مشابه
A Comparison Between Fourier Transform Adomian Decomposition Method and Homotopy Perturbation ethod for Linear and Non-Linear Newell-Whitehead-Segel Equations
In this paper, a comparison among the hybrid of Fourier Transform and AdomianDecomposition Method (FTADM) and Homotopy Perturbation Method (HPM) is investigated.The linear and non-linear Newell-Whitehead-Segel (NWS) equations are solved and the results arecompared with the exact solution. The comparison reveals that for the same number of componentsof recursive sequences, the error of FTADM is ...
متن کاملDynamics of an Interface Connecting a Stripe Pattern and a Uniform State: amended Newell-Whitehead-Segel equation
The dynamics of an interface connecting a stationary stripe pattern with a homogeneous state is studied. The conventional approach which describes this interface, Newell–Whitehead–Segel amplitude equation, does not account for the rich dynamics exhibited by these interfaces. By amending this amplitude equation with a nonresonate term, we can describe this interface and its dynamics in a unified...
متن کاملSystematic derivation of a rotationally covariant extension of the two-dimensional Newell-Whitehead-Segel equation.
An extension of the Newell-Whitehead-Segel amplitude equation covariant under abritrary rotations is derived systematically by the renormalization group method. Typeset using REVTEX 1 The present day theory of pattern formation to a large degree rests on the derivation and exploitation of amplitude equations. In particular, for the formation of 2-dimensional patterns by spontaneous symmetry bre...
متن کاملCanonical reduction of self-dual Yang–Mills equations to Fitzhugh–Nagumo equation and exact solutions
The (constrained) canonical reduction of four-dimensional self-dual Yang–Mills theory to two-dimensional Fitzhugh–Nagumo and the real Newell–Whitehead equations are considered. On the other hand, other methods and transformations are developed to obtain exact solutions for the original two-dimensional Fitzhugh–Nagumo and Newell– Whitehead equations. The corresponding gauge potential Al and the ...
متن کاملPeriodic Nucleation Solutions of the Real Ginzburg-Landau equation in a Finite Box
In the vicinity of the threshold of a continuous pattern-forming instability a description of the basic periodic solution and its slow modulations is possible by perturbation theory [Newell & Whitehead, 1969; Segel, 1969; Stuart & Di Prima, 1978]. For quasi-one-dimensional, stationary, and periodic patterns formed from an unstructured state through a continuous soft-mode finite-q instability, a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1996