Mapping between Nonlinear Schödinger Equations with Real and Complex Potentials
نویسنده
چکیده
Communicated by XXX Abstract. A mapping between stationary solutions of nonlinear Schödinger equations with real and complex potentials is constructed and a set of exact solutions with real energies are obtained for a large class of complex potentials. As specific examples we consider the case of the damped dynamics of a quantum harmonic oscillator and the case of dissipative periodic soliton solutions of the nonlinear Schrödinger equation with complex potential.
منابع مشابه
Mapping between Nonlinear Schrödinger Equations with Real and Complex Potentials
A mapping between the stationary solutions of nonlinear Schrödinger equations with real and complex potentials is constructed and a set of exact solutions with real energies are obtained for a large class of complex potentials. As specific examples we consider the case of dissipative periodic soliton solutions of the nonlinear Schrödinger equation with complex potential.
متن کاملThe existence results for a coupled system of nonlinear fractional differential equations with multi-point boundary conditions
In this paper, we study a coupled system of nonlinear fractional differential equations with multi-point boundary condi- tions. The differential operator is taken in the Riemann-Liouville sense. Applying the Schauder fixed-point theorem and the contrac- tion mapping principle, two existence results are obtained for the following system D^{alpha}_{0+}x(t)=fleft(t,y(t),D^{p}_{0+}y(t)right), t in (0,...
متن کاملSOLVING FRACTIONAL NONLINEAR SCHR"{O}DINGER EQUATIONS BY FRACTIONAL COMPLEX TRANSFORM METHOD
In this paper, we apply fractional complex transform to convert the fractional nonlinear Schr"{o}dinger equations to the nonlinear Schr"{o}dinger equations.
متن کاملSome Fixed Point Theorems in Generalized Metric Spaces Endowed with Vector-valued Metrics and Application in Linear and Nonlinear Matrix Equations
Let $mathcal{X}$ be a partially ordered set and $d$ be a generalized metric on $mathcal{X}$. We obtain some results in coupled and coupled coincidence of $g$-monotone functions on $mathcal{X}$, where $g$ is a function from $mathcal{X}$ into itself. Moreover, we show that a nonexpansive mapping on a partially ordered Hilbert space has a fixed point lying in the unit ball of the Hilbert space. ...
متن کاملGroup classification of (1+1)-Dimensional Schrödinger Equations with Potentials and Power Nonlinearities
We perform the complete group classification in the class of nonlinear Schrödinger equations of the form iψt+ψxx+|ψ|ψ+V (t, x)ψ = 0 where V is an arbitrary complex-valued potential depending on t and x, γ is a real non-zero constant. We construct all the possible inequivalent potentials for which these equations have non-trivial Lie symmetries using a combination of algebraic and compatibility ...
متن کامل