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Full-Text Articles in Physical Sciences and Mathematics
Counter-Propagating Two-Soliton Solutions In The Fermi–Pasta–Ulam Lattice, Aaron Hoffman, C.E. Wayne
Counter-Propagating Two-Soliton Solutions In The Fermi–Pasta–Ulam Lattice, Aaron Hoffman, C.E. Wayne
Aaron Hoffman
We study the interaction of small amplitude, long-wavelength solitary wavesin the Fermi–Pasta–Ulam model with general nearest-neighbour interactionpotential. We establish global-in-time existence and stability of counterpropagatingsolitary wave solutions. These solutions are close to the linearsuperposition of two solitary waves for large positive and negative values oftime; for intermediate values of time these solutions describe the interactionof two counter-propagating pulses. These solutions are stable with respectto perturbations in L2 and asymptotically stable with respect to perturbationswhich decay exponentially at spatial ±∞.
Fall 2010 Mth 2140: Differential Equations: Course Materials: Homework 3, Aaron Hoffman
Fall 2010 Mth 2140: Differential Equations: Course Materials: Homework 3, Aaron Hoffman
Aaron Hoffman
An introduction to the solution techniques of differential equations. Topics include mathematical modeling, solution techniques to linear and nonlinear first-order differential equations, characteristic solutions to linear constant coefficient second-order differential equations, solutions to homogeneous (unforced) and inhomogeneous (forced) second-order linear systems. Applications include modeling of physical systems.
Fall 2010 Mth 2140: Differential Equations: Course Materials: Final, Aaron Hoffman
Fall 2010 Mth 2140: Differential Equations: Course Materials: Final, Aaron Hoffman
Aaron Hoffman
An introduction to the solution techniques of differential equations. Topics include mathematical modeling, solution techniques to linear and nonlinear first-order differential equations, characteristic solutions to linear constant coefficient second-order differential equations, solutions to homogeneous (unforced) and inhomogeneous (forced) second-order linear systems. Applications include modeling of physical systems.
Fall 2010 Mth 2140: Differential Equations: Course Materials: Homework 1, Aaron Hoffman
Fall 2010 Mth 2140: Differential Equations: Course Materials: Homework 1, Aaron Hoffman
Aaron Hoffman
An introduction to the solution techniques of differential equations. Topics include mathematical modeling, solution techniques to linear and nonlinear first-order differential equations, characteristic solutions to linear constant coefficient second-order differential equations, solutions to homogeneous (unforced) and inhomogeneous (forced) second-order linear systems. Applications include modeling of physical systems.
Fall 2010 Mth 2140: Differential Equations: Course Materials: Homework 2, Aaron Hoffman
Fall 2010 Mth 2140: Differential Equations: Course Materials: Homework 2, Aaron Hoffman
Aaron Hoffman
An introduction to the solution techniques of differential equations. Topics include mathematical modeling, solution techniques to linear and nonlinear first-order differential equations, characteristic solutions to linear constant coefficient second-order differential equations, solutions to homogeneous (unforced) and inhomogeneous (forced) second-order linear systems. Applications include modeling of physical systems.
Fall 2010 Mth 2140: Differential Equations: Information About Course: Course Syllabus, Aaron Hoffman
Fall 2010 Mth 2140: Differential Equations: Information About Course: Course Syllabus, Aaron Hoffman
Aaron Hoffman
An introduction to the solution techniques of differential equations. Topics include mathematical modeling, solution techniques to linear and nonlinear first-order differential equations, characteristic solutions to linear constant coefficient second-order differential equations, solutions to homogeneous (unforced) and inhomogeneous (forced) second-order linear systems. Applications include modeling of physical systems.