Wavelet-inspired approaches for localized solutions of nonlinear partial differential equations (NDPE) were presented. A multi-scale similarity analysis was used which gives specific relations between the velocity, amplitude and width of localized solutions of nonlinear differential equations. This approach does not need the explicit form of the exact solutions.
Publication Source (Journal or Book title)
Mathematics and Computers in Simulation
Ludu, A., O'Connell, R., & Draayer, J. (2003). Nonlinear equations and wavelets. Mathematics and Computers in Simulation, 62 (1-2), 91-99. https://doi.org/10.1016/S0378-4754(02)00183-0