Highly Influenced

# Analyticity of Solutions of the Generalized Korteweg-de Vries Equation with Respect to Their Initial Values

@inproceedings{Zhang1995AnalyticityOS, title={Analyticity of Solutions of the Generalized Korteweg-de Vries Equation with Respect to Their Initial Values}, author={Bing-Yu Zhang}, year={1995} }

- Published 1995

It is shown that the initial value problem (IVP) of the generalized KdV equation @tu + @x(a(u)) + @ 3 xu = 0; u(x; 0) = (x) is well posed in the classical Sobolev space H(R) with s > 3=4, which thus establishes a nonlinear map K from H(R) to C([ T; T ];H(R)). Then it is proved that (i) if a = a(x) is a C function on R to R, then K is in nitely many times Frechet di erentiable; (ii) if a = a(x) is a polynomial, then K is analytic, i.e. for any 2 H(R), K has a Taylor series expansionÂ

#### From This Paper

##### Figures, tables, results, connections, and topics extracted from this paper.

20 Extracted Citations

31 Extracted References

Similar Papers