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- W2786790413 abstract "We develop a method for generating solutions to large classes of evolutionary partial differential systems with non-local nonlinearities. For arbitrary initial data, the solutions are generated from the corresponding linearized equations. The key is a Fredholm integral equation relating the linearized flow to an auxiliary linear flow. It is analogous to the Marchenko integral equation in integrable systems. We show explicitly how this can be achieved through several examples including reaction–diffusion systems with non-local quadratic nonlinearities and the nonlinear Schrodinger equation with a non-local cubic nonlinearity. In each case, we demonstrate our approach with numerical simulations. We discuss the effectiveness of our approach and how it might be extended. This article is part of the theme issue ‘Stability of nonlinear waves and patterns and related topics’." @default.
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- W2786790413 date "2018-01-01" @default.
- W2786790413 modified "2023-09-26" @default.
- W2786790413 title "Matlab file for Riccati RDE solution from Partial differential systems with non-local nonlinearities: generation and solutions" @default.
- W2786790413 doi "https://doi.org/10.6084/m9.figshare.5831454.v1" @default.
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