Soliton Dynamics for the Nonlinear Schrödinger Equation with Magnetic Field
نویسندگان
چکیده
Abstract. The semiclassical regime of a nonlinear focusing Schrödinger equation in presence of non-constant electric and magnetic potentials V, A is studied by taking as initial datum the ground state solution of an associated autonomous stationary equation. The concentration curve of the solutions is a parameterization of the solutions of the second order ordinary equation ẍ = −∇V (x) − ẋ × B(x), where B = ∇ × A is the magnetic field of a given magnetic potential A.
منابع مشابه
Soliton Dynamics for Fractional Schrödinger Equations
We investigate the soliton dynamics for the fractional nonlinear Schrödinger equation by a suitable modulational inequality. In the semiclassical limit, the solution concentrates along a trajectory determined by a Newtonian equation depending of the fractional diffusion parameter.
متن کاملSemiclassically Concentrates Waves for the Nonlinear Schrödinger Equation with External Field
Classes of solutions, asymptotic in small parameter , → 0, are constructed to the generalized nonlinear Schrödinger equation (NSE) in a multi-dimensional space with an external field in the framework of the WKB-Maslov method. Asymptotic semiclassically concentrated solutions (SCS), regarded as multi-dimensional solitary waves, are introduced for the NSE with an external field and cubic local no...
متن کاملMulti-soliton of the (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff equation and KdV equation
A direct rational exponential scheme is offered to construct exact multi-soliton solutions of nonlinear partial differential equation. We have considered the Calogero–Bogoyavlenskii–Schiff equation and KdV equation as two concrete examples to show efficiency of the method. As a result, one wave, two wave and three wave soliton solutions are obtained. Corresponding potential energy of the solito...
متن کاملThree-Dimensional Bright–Dark Soliton, Bright Soliton Pairs, and Rogue Wave of Coupled Nonlinear Schrödinger Equation with Time–Space Modulation
We systematically provide a similarity transformation reducing the (3 + 1)-dimensional inhomogeneous coupled nonlinear Schrödinger (CNLS) equation with variable coefficients and parabolic potential to the (1 + 1)-dimensional coupled nonlinear Schrödinger equation with constant coefficients. Based on the similarity transformation, we discuss the dynamics of the propagation of the three-dimension...
متن کاملDeterminant Form of Dark Soliton Solutions of the Discrete Nonlinear Schrödinger Equation
It is shown that the N-dark soliton solutions of the integrable discrete nonlinear Schrödinger (IDNLS) equation are given in terms of the Casorati determinant. The conditions for reduction, complex conjugacy and regularity for the Casorati determinant solution are also given explicitly. The relationship between the IDNLS and the relativistic Toda lattice is discussed.
متن کامل