Burde, G.I. and Sergyeyev, A. (2013) Ordering of Two Small Parameters in the Shallow Water Wave Problem. Journal of Physics A: Mathematical and Theoretical, 46, Article ID: 075501.

has been cited by the following article:

• TITLE: Martingale Solution to Stochastic Extended Korteweg-de Vries Equation

  AUTHORS: Anna Karczewska, Maciej Szczeciński

  KEYWORDS: Extended Korteweg-de Vries Equation, Martingale Solution, Stochastic Fluid Dynamics

  JOURNAL NAME: Advances in Pure Mathematics, Vol.8 No.12, December 26, 2018

  ABSTRACT: The deterministic extended Korteweg-de Vries equation plays an essential role in the description of the creation and propagation of nonlinear waves in many fields. We study a stochastic extended Korteweg-de Vries equation driven by a multiplicative noise in the form of a cylindrical Wiener process. We prove the existence of a martingale solution to the equation studied for all physically relevant initial conditions. The proof of the solution is based on two approximations of the problem considered and the compactness method.