Higher-Order Nonlinear Dispersive Equations
نویسندگان
چکیده
منابع مشابه
On the Cauchy problem for higher-order nonlinear dispersive equations
We study the higher-order nonlinear dispersive equation ∂tu+ ∂ 2j+1 x u = ∑ 0≤j1+j2≤2j aj1,j2∂ j1 x u∂ j2 x u, x, t ∈ R. where u is a real(or complex-) valued function. We show that the associated initial value problem is well posed in weighted Besov and Sobolev spaces for small initial data. We also prove ill-posedness results when a0,k 6= 0 for some k > j, in the sense that this equation cann...
متن کاملStability of Compacton Solutions of Fifth-Order Nonlinear Dispersive Equations
We consider fifth-order nonlinear dispersive K(m,n, p) type equations to study the effect of nonlinear dispersion. Using simple scaling arguments we show, how, instead of the conventional solitary waves like solitons, the interaction of the nonlinear dispersion with nonlinear convection generates compactons the compact solitary waves free of exponential tails. This interaction also generates ma...
متن کاملDecay Properties for Solutions of Fifth Order Nonlinear Dispersive Equations
We consider the initial value problem associated to a large class of fifth order nonlinear dispersive equations. This class includes several models arising in the study of different physical phenomena. Our aim is to establish special (space) decay properties of solutions to these systems. These properties complement previous unique continuation results and in some case, show that they are optim...
متن کاملHigher-order Iterative Algorithms for Solving Nonlinear Equations
In this paper, we use the new decomposition technique to suggest and analyze new iterative methods for solving nonlinear equations. Our technique of developing these iterative methods is very simple as compared with other techniques. We prove the eighth order convergence of the proposed method. Various numerical examples are given to illustrate the performance of the new method.
متن کاملForced oscillation of higher-order nonlinear differential equations
Some new criteria have been established for the oscillation of higher-order forced nonlinear differential equation of the form Lnx(t) + q(t)F(x(t)) = e(t) according to the smart choice of a class of new auxiliary functions. No restriction is imposed on the forcing term e(t) as those assumed in [A.G. Kartsatos, Maintenance of oscillations under the effect of a periodic forcing term, Proc. Amer. ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1994
ISSN: 0002-9939
DOI: 10.2307/2160855