Abstract:
Schrödinger equations containing a nonlinear integral term are considered. For some types of “self-interaction potential” an exact solution of soliton type is constructed. An example is given for obtaining an almost-solution in the asymptotic sense by means of harmonic approximation of the potential. A diagram technique is proposed for solving the Cauchy problem perturbatively.
Citation:
Vo Khan' Fuk, V. M. Chetverikov, “Generalized solitons of the Schrödinger equation with unitary nonlinearity”, TMF, 36:3 (1978), 345–351; Theoret. and Math. Phys., 36:3 (1978), 779–783
This publication is cited in the following 6 articles:
A. L. Lisok, A. Yu. Trifonov, A. V. Shapovalov, “Symmetry operators of a Hartree-type equation with quadratic potential”, Siberian Math. J., 46:1 (2005), 119–132
A. L. Lisok, A. Yu. Trifonov, A. V. Shapovalov, “Green's Function of a Hartree-Type Equation with a Quadratic Potential”, Theoret. and Math. Phys., 141:2 (2004), 1528–1541
Lisok, AL, “The evolution operator of the Hartree-type equation with a quadratic potential”, Journal of Physics A-Mathematical and General, 37:16 (2004), 4535
V. P. Maslov, “Semiclassical asymptotics of the eigenfunctions of the Schrödinger-Hartree equation. New form of classical self-consistent field”, Theoret. and Math. Phys., 99:1 (1994), 484–493
V. M. Olkhov, “Soliton solutions to equations with inertial nonlinearity”, Theoret. and Math. Phys., 51:1 (1982), 414–415
V. P. Maslov, A. M. Chebotarev, “Path integral over branching paths”, Theoret. and Math. Phys., 45:3 (1980), 1058–1069
Citation in format AMSBIB
Contact us: