arXiv:1509.09272 Abstract | arXiv Analytics

arXiv:1509.09272 [math.AP]Abstract References Reviews Resources

On stationary solutions of KdV and mKdV equations

Published 2015-09-30Version 1

Stationary solutions on a bounded interval for an initial-boundary value problem to Korteweg--de~Vries and modified Korteweg--de~Vries equation (for the last one both in focusing and defocusing cases) are constructed. The method of the study is based on the theory of conservative systems with one degree of freedom. The obtained solutions turn out to be periodic. Exact relations between the length of the interval and coefficients of the equations which are necessary and sufficient for existence of nontrivial solutions are established.

Comments: 8 pages

Categories: math.AP

Subjects: 35Q53

Keywords: stationary solutions, mkdv equations, initial-boundary value problem, solutions turn, nontrivial solutions

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