Traveling wave solutions to the Allen–Cahn equation
نویسندگان
چکیده
For the Allen-Cahn equation, it is well known that there a monotone standing wave joining with balanced wells of potential. In this paper we study existence traveling solutions for equation on an infinite channel. Such possess large number oscillation and they are obtained aid variational arguments.
منابع مشابه
Traveling solitary wave solutions to the generalized Boussinesq equation
In this paper, we are concerned with the generalized Boussinesq equation including the singularly sixth-order Boussinesq equation, which describes the bi-directional propagation of small amplitude and long capillary-gravity waves on the surface of shallow water for bond number less than but very close to 1/3. By the means of two proper ansatzs, we obtain explicit traveling solitary wave solutio...
متن کاملStability of traveling wave solutions to the Whitham equation
Article history: Received 21 December 2013 Received in revised form 19 April 2014 Accepted 23 April 2014 Available online 14 May 2014 Communicated by C.R. Doering
متن کاملBK Equation and Traveling Wave Solutions
It has been shown that the transition to the saturation regime of high energy QCD is similar to the formation of the front of a traveling wave. In particular, it can be verified that Balitsky-Kovchegov (BK) evolution equation reduces, after some approximations, to the nonlinear Fisher and Kolmogorov-Petrovsky-Piscounov (FKPP) equation, well-known from statistical physics. In these proceedings, ...
متن کاملSome traveling wave solutions of soliton family
Solitons are ubiquitous and exist in almost every area from sky to bottom. For solitons to appear, the relevant equation of motion must be nonlinear. In the present study, we deal with the Korteweg-deVries (KdV), Modied Korteweg-de Vries (mKdV) and Regularised LongWave (RLW) equations using Homotopy Perturbation method (HPM). The algorithm makes use of the HPM to determine the initial expansion...
متن کاملMeromorphic traveling wave solutions of the Kuramoto–Sivashinsky equation
We determine all cases when there exists a meromorphic solution of the ODE νw + bw + μw + w/2 +A = 0. This equation describes traveling waves solutions of the KuramotoSivashinsky equation. It turns out that there are no other meromorphic solutions besides those explicit solutions found by Kuramoto and Kudryashov. The general method used in this paper, based on Nevanlinna theory, is applicable t...
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: Annales de l'Institut Henri Poincaré C, Analyse non linéaire
سال: 2022
ISSN: ['0294-1449', '1873-1430']
DOI: https://doi.org/10.4171/aihpc/23