Computing the Solution of the m-Korteweg-de Vries Equation on Turing Machines

Authors:
Dianchen Lu;Qingyan Wang
Affiliations:
Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang, P.R. China;Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang, P.R. China
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2008

Citing 3
Cited 0

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Abstract

In this paper, we study the initial value problem of the mKdV equation, and convert the constant coefficients mKdV equation into its standard norm by linear transformation. Then, we define a nonlinear map K"R:H^s(R)-C(R,H^s(R))(s=14), from the initial data to the solution of the equation, and prove K"R is Turing computable for any integer s=3. Therefore, the solution of the mKdV equation with arbitrary precision on Turing machines can be satisfied.