Analyticity and smoothing effect for the fifth order KdV type equation
نویسندگان
چکیده
منابع مشابه
Exp-function method for the exact solutions of fifth order KdV equation and modified Burgers equation
We discuss the recent paper by Inan and Ugurlu [Inan I.E., Ugurlu Y., Exp-function method for the exact solutions of fifth order KdV equation and modified Burgers equation, Appl. Math. Comp. 217 (2010) 1294 – 1299]. We demonstrate that all exact solutions of fifth order KdV equation and modified Burgers equation by Inan and Ugurlu are trivial solutions that are reduced to constants. Moreover, w...
متن کاملOrder reduction and μ-conservation law for the non-isospectral KdV type equation a with variable-coefficients
The goal of this paper is to calculate of order reduction of the KdV typeequation and the non-isospectral KdV type equation using the μ-symmetrymethod. Moreover we obtain μ-conservation law of the non-isospectral KdVtype equation using the variational problem method.
متن کاملLow regularity solutions of two fifth-order KdV type equations
The Kawahara and modified Kawahara equations are fifth-order KdV type equations and have been derived to model many physical phenomena such as gravitycapillary waves and magneto-sound propagation in plasmas. This paper establishes the local well-posedness of the initial-value problem for Kawahara equation in H(R) with s > − 4 and the local well-posedness for the modified Kawahara equation in H(...
متن کاملNon-Analyticity in Time of Solutions to the KdV Equation
It is proved that formal power series solutions to the initial value problem ∂tu = ∂ 3 xu + ∂x(u ), u(0, x) = φ(x) with analytic data φ belong to the Gevrey class G in time. However, if φ(x) = 1 1+x2 , the formal solution does not belong to the Gevrey class G in time for 0 ≤ s < 2, so it is not analytic in time. The proof is based on the estimation of a double sum of products of binomial coeffi...
متن کاملTwo-pulse Solutions in the Fifth-order Kdv Equation: Rigorous Theory and Numerical Approximations
We revisit existence and stability of two-pulse solutions in the fifth-order Korteweg–de Vries (KdV) equation with two new results. First, we modify the Petviashvili method of successive iterations for numerical (spectral) approximations of pulses and prove convergence of iterations in a neighborhood of two-pulse solutions. Second, we prove structural stability of embedded eigenvalues of negati...
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 Japan Academy, Series A, Mathematical Sciences
سال: 2010
ISSN: 0386-2194
DOI: 10.3792/pjaa.86.101