## Quasiclassical integral equations and the asymptotic behavior of solutions to the Korteweg-de Vries equation for large times.(English. Russian original)Zbl 0956.35114

Dokl. Math. 53, No. 3, 441-444 (1996); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 348, No. 4, 455-458 (1996).
The authors study the asymptotic behavior of the solution $$u(x,t)$$ for $$t\to\infty$$ to the Cauchy problem to the Korteweg-de Vries equation $u_t= u_{xxx}+ 6uu_x,\quad u|_{t= 0}= u_0,\quad u\in\mathbb{R},\quad t\geq 0$ using its well-known connection to the spectral problem for the Schrödinger equation $\psi_{xx}+ v\psi+ k^2\psi= 0$ (inverse problem method).

### MSC:

 35Q53 KdV equations (Korteweg-de Vries equations) 37K15 Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems