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Karczewska, A., Rozmej, P., Infeld, E. and Rowlands, G. (2017) Adiabatic Invariants of the Extended KdV Equation. Physics Letters A, 381, 270-275.
https://doi.org/10.1016/j.physleta.2016.11.035

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.