Quantitative constructive representation of the KdV flow in $H^3$ via $L^2$-energy-preserving centered-difference Chernoff approximations and Picard iteration

Comlan Edmond Koudjinan

We give a constructive representation of the solution of the KdV equation $u_t=-u_{xxx}+6u{u}_x$ on $\mathbb{R}$ for real initial data in $H^3(\mathbb{R})$. The approximations couple a…