TY - GEN

T1 - On the modified Korteweg - de Vries equation

AU - Hayashi, Nakao

AU - Naumkin, Pavel

PY - 1999/1/1

Y1 - 1999/1/1

N2 - We consider the large time asymptotic behavior of solutions to the Cauchy problem for the modified Korteweg - de Vries equation ut + a(t) (u3)x + 1/3Uxxx = O,(t,r) ϵR x R, with initial data u(0,z) = q1(z),z ϵ R.. We assume that the coefficient a(t) ϵ C1(R) is real, bounded and slowly varying function, such that /a'(t)≤C(l + /t/)-7/6. We suppose that the iriitial dah are real ~ valued and small enough, belonging to the weighted Sobolev space. We prove the time decay estimates of the solutims.We also fiud the asympt,otics for large time of the solution in the neighborhood of the self-similar solution.

AB - We consider the large time asymptotic behavior of solutions to the Cauchy problem for the modified Korteweg - de Vries equation ut + a(t) (u3)x + 1/3Uxxx = O,(t,r) ϵR x R, with initial data u(0,z) = q1(z),z ϵ R.. We assume that the coefficient a(t) ϵ C1(R) is real, bounded and slowly varying function, such that /a'(t)≤C(l + /t/)-7/6. We suppose that the iriitial dah are real ~ valued and small enough, belonging to the weighted Sobolev space. We prove the time decay estimates of the solutims.We also fiud the asympt,otics for large time of the solution in the neighborhood of the self-similar solution.

UR - http://www.scopus.com/inward/record.url?scp=85041472525&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85041472525&partnerID=8YFLogxK

U2 - 10.1109/DD.1999.816195

DO - 10.1109/DD.1999.816195

M3 - Conference contribution

AN - SCOPUS:85041472525

T3 - International Seminar: Day on Diffraction - Proceedings

SP - 146

EP - 156

BT - International Seminar

A2 - Grikuro, V.E.

A2 - Babic, V.M.

A2 - Androno, I.V.

A2 - Buldyrev, V.S.

A2 - Kiselev, A.P.

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - International Seminar: Day on Diffraction, IS-DoD 1999

Y2 - 1 June 1999 through 3 June 1999

ER -