A moving average transform in the plane with a variable size and shape window depending on the position and the ’time’ is studied. The main objective is to select the window parameters in such a way that the new transform converges smoothly to the identity transform at the boundary of a prescribed bounded plane region. A new approximation of solitary waves arising from Korteweg-de Vries equation is obtained based on results in the paper. Numerical implementation and examples are included.
Vatchev, Vesselin, "Variable Moving Average Transform Stitching Waves" (2016). Mathematical and Statistical Sciences Faculty Publications and Presentations. 1.
Mathematical Modelling of Natural Phenomena