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Solitons , Shockwaves and Spikes : Computational Simulation of Nonlinear Waves on Lattice
| Content Provider | Semantic Scholar |
|---|---|
| Author | Srihari Y. Sritharan |
| Abstract | Abstract In this paper, we systematically find computational solutions to a class of differential equation systems which exhibit nonlinear wave behavior. After discretizing the nonlinear partial differential equations, we got nonlinear dynamical systems on a lattice. Using MATLAB, we utilized both an ODE and Algorithm solver method to get explicit solutions with soliton and shockwave behavior. Using a 64 particle model, we plotted and animated our results in several forms, including a linear lattice, a ring lattice (when appropriate) and phase plots. Furthermore, our use of an algorithm solver yielded three-dimensional plots of shockwave evolution. Our calculations include the Fermi-Pasta-Ulam model, the Toda Exponential Lattice, the Inviscid Burgers Equation and the Hodgkin-Huxley Model. Using previously calculated lattices, we experimented with controls and feedbacks, including the Sine-Gordon Equation and the Gabov-Shefter Rosales integro-differential equation. We concluded our research with Split Domain calculations and the introduction of a memory-less computation method. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.m-hikari.com/ams/ams-password-2009/ams-password57-60-2009/sritharanAMS57-60-2009.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
