Abstract:
An existence and uniqueness theorem is proved for the solution of
the Cauchy problem for the nonlinear Schrödinger equation with
repulsion in the class of functions with singularities of the type
$x^{-1}$. The behavior of the singularity lines of the solution in
the $(x,t)$ plane is described.
Citation:
V. A. Arkad'ev, “Application of inverse scattering method to singular solutions of nonlinear equations. III”, TMF, 58:1 (1984), 38–49; Theoret. and Math. Phys., 58:1 (1984), 24–32
This publication is cited in the following 8 articles:
A. A. Raskovalov, A. A. Gelash, “Resonanse interaction of breathers in the Manakov system”, Theoret. and Math. Phys., 213:3 (2022), 1669–1685
Sakhnovich, A, “Dirac type system on the axis: explicit formulae for matrix potentials with singularities and soliton-positon interactions”, Inverse Problems, 19:4 (2003), 845
Alexander Sakhnovich, “Generalized Bäcklund–Darboux Transformation: Spectral Propertiesand Nonlinear Equations”, Journal of Mathematical Analysis and Applications, 262:1 (2001), 274
V. O. Tarasov, “Boundary-value problem for the nonlinear Schr�dinger equation”, J Math Sci, 54:3 (1991), 958
I. T. Habibullin, A. G. Shagalov, “Numerical realization of the inverse scattering method”, Theoret. and Math. Phys., 83:3 (1990), 565–573
P. N. Bibikov, V. O. Tarasov, “Boundary-value problem for nonlinear Schrödinger equation”, Theoret. and Math. Phys., 79:3 (1989), 570–579
Ludwig D. Faddeev, Leon A. Takhtajan, Hamiltonian Methods in the Theory of Solitons, 1987, 356
V. A. Arkad'ev, A. K. Pogrebkov, M. K. Polivanov, “Singular solutions of the KdV equation and the inverse scattering method”, J Math Sci, 31:6 (1985), 3264
Citation in format AMSBIB
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