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Karczewska, A., Rozmej, P. and Infeld, E. (2015) Energy Invariant for Shallow-Water Waves and the Korteweg-de Vries Equation: Doubts about the Invariance of Energy. Physical Review E, 92, Article ID: 053202.
https://doi.org/10.1103/PhysRevE.92.053202

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.