Petar Y. Topalov
Mikhail Shubin, Robert C. McOwen, Maxim Braverman, Emma Previato
Date of Award
Doctor of Philosophy
Department or Academic Unit
College of Arts and Sciences. Department of Mathematics.
asymptotic expansion, discretization, finite difference, formal solution, Korteweg-De Vries, unbounded solutions
In this dissertation we prove local existence and uniqueness of solutions of the focusing modified Korteweg - de Vries equation ut + u2ux + uxxx = 0 in classes of unbounded functions that admit an asymptotic expansion at infinity in decreasing powers of x. We show that an asymptotic solution differs from a genuine solution by a smooth function that is of Schwartz class with respect to x and that solves a generalized version of the focusing mKdV equation. The latter equation is solved by discretization methods.
Gonzalez, John, "Unbounded solutions of the modified Korteweg-De Vries equation" (2010). Mathematics Dissertations. Paper 16. http://hdl.handle.net/2047/d20000881
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