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Boundary value problem for the KdV equation on a half-line. (English. Russian original) Zbl 0916.35100
Theor. Math. Phys. 110, No. 1, 78-90 (1997); translation from Teor. Mat. Fiz. 110, No. 1, 98-113 (1997).
Summary: The Lax pair corresponding to the boundary value problem with the condition \(u|_{x= 0}= a\) for the KdV equation is presented. A broad class of exact solutions to this equation is constructed and the conservation laws are discussed.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
35R30 Inverse problems for PDEs
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