Travelling wave solutions to a perturbed Korteweg-de Vries equation
نویسندگان
چکیده
منابع مشابه
Symbolic Computation and Non-travelling Wave Solutions of the (2+1)-Dimensional Korteweg de Vries Equation
In this paper, with the aid of symbolic computation we improve the extended F-expansion method described in Chaos, Solitons and Fractals 22, 111 (2004) to solve the (2 +1)-dimensional Korteweg de Vries equation. Using this method, we derive many exact non-travelling wave solutions. These are more general than the previous solutions derived with the extended F-expansion method. They include the ...
متن کاملChaotic behaviour of the solutions to a perturbed Korteweg-de Vries equation
Stationary wave solutions of the perturbed Korteweg-de Vries equation are considered in the presence of external hamiltonian perturbations. Conditions of their chaotic behaviour are studied with the help of Melnikov theory. For the homoclinic chaos Poincaré sections are constructed to demonstrate the complicated behaviour, and Lyapunov exponents are also numerically calculated.
متن کاملTravelling-Wave Solutions for Korteweg-de Vries-Burgers Equations through Factorizations
Travelling-wave solutions of the standard and compound form of Kortewegde Vries-Burgers equations are found using factorizations of the corresponding reduced ordinary differential equations. The procedure leads to solutions of Bernoulli equations of nonlinearity 3/2 and 2 (Riccati), respectively. Introducing the initial conditions through an imaginary phase in the travelling coordinate, we obta...
متن کاملKorteweg - de Vries Equation ; Asymptotic Behavior of Solutions
In [9] and [10], we have studied the initial value problem for the Korteweg-de Vries (KdV) equation (1.1) ut—6uu x +u xxx =0 by the inverse scattering method. In this paper we study the asymptotic behavior of the solutions as t— >zh°°-Consider the Schrodinger equation (1.2) over (— oo } oo) with the potential u(x) satisfying (1.3) (throughout the paper integration is taken over (— oo, oo) unles...
متن کاملUnbounded Solutions of the Modified Korteweg-De Vries Equation
Abstract We prove local existence and uniqueness of solutions of the focusing modified Korteweg de Vries equation ut+u 2 ux+uxxx = 0 in classes of unbounded functions that admit an asymptotic expansion at infinity in decreasing powers of x. We show that an asymptotic solution differs from a genuine solution by a smooth function that is of Schwartz class with respect to x and that solves a gener...
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: Hiroshima Mathematical Journal
سال: 1994
ISSN: 0018-2079
DOI: 10.32917/hmj/1206128032