Mapping between Nonlinear Schrödinger Equations with Real and Complex Potentials
نویسندگان
چکیده
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.
منابع مشابه
Mapping between Nonlinear Schödinger Equations with Real and Complex Potentials
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 s...
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 کاملRepresentation Formula for Stochastic Schrödinger Evolution Equations and Applications
We prove a representation formula for solutions of Schrödinger equations with potentials multiplied by a temporal real-valued white noise in the Stratonovich sense. Using this formula, we obtain a dispersive estimate which allows us to study the Cauchy problem in L or in the energy space of model equations arising in Bose Einstein condensation [1] or in fiber optics [2]. Our results also give a...
متن کاملConditions and Stability Analysis for Saddle-Node Bifurcations of Solitary Waves in Generalized Nonlinear Schrödinger Equations
Saddle-node bifurcations of solitary waves in generalized nonlinear Schrödinger equations with arbitrary forms of nonlinearity and external potentials in arbitrary spatial dimensions are analyzed. First, general conditions for these bifurcations are derived. Second, it is shown analytically that the linear stability of these solitary waves does not switch at saddle-node bifurcations, which is i...
متن کاملGlobal Existence Results for Nonlinear Schrödinger Equations with Quadratic Potentials
We prove that no finite time blow up can occur for nonlinear Schrödinger equations with quadratic potentials, provided that the potential has a sufficiently strong repulsive component. This is not obvious in general, since the energy associated to the linear equation is not positive. The proof relies essentially on two arguments: global in time Strichartz estimates, and a refined analysis of th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013