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Diffraction in a nonlinear defocusing medium. (English. Russian original) Zbl 0741.35078
J. Sov. Math. 57, No. 3, 3078-3083 (1991); translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 179, 23-31 (1989).
See the review in Zbl 0706.35125.

MSC:
35Q55 NLS equations (nonlinear Schrödinger equations)
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35Q15 Riemann-Hilbert problems in context of PDEs
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References:
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[2] M. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform, SIAM, Philadelphia, Pa. (1981). · Zbl 0472.35002
[3] A. R. Its and A. F. Ustinov, ?Time asymptotics of the nonlinear Schrödinger equation with ?finite density? boundary conditions,? Dokl. Akad. Nauk SSSR,291, No. 1, 91?95 (1986). · Zbl 0651.35015
[4] V. P. Kotlyarov, ?Asymptotic solitons of the nonlinear Schrödinger equation,? Preprint No. 39, FTINT Akad. Nauk Ukr. SSR, Kharkov (1986).
[5] R. F. Bikbaev,?The KdV equation with finite-zone boundary conditions,? Preprint, BNTS Univ. (1988).
[6] R. F. Bikbaev, ?Time asymptotics of the NS equation with boundary conditions of the?step? type,? Teoret. Mat. Fiz.,81, No. 2, 37?52 (1989). · Zbl 0702.35231
[7] R. F. Bikbaev, ?On the asymptotics ast ? ? of the solution of the Cauchy problem for the L-L equation,? Teoret. Mat. Fiz.,77, No. 2, 163?171 (1988).
[8] R. F. Bikbaev and V. Yu. Novokshenov (V. Ju. Novokshenov), ?Self-similar solutions of Whitham equations,? in: Proc. III Intern. Workshop, Vol. 1, Kiev (1988), pp. 32?35.
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