Abstract
Using Lie group theory and canonical transformations, we construct explicit solutions of nonlinear Schrodinger equations with spatially inhomogeneous nonlinearities. We present the general theory, use it to study different examples and use the qualitative theory of dynamical systems to obtain some properties of these solutions.
Highlights
The Nonlinear Schrodinger Equation (NLSE) in its many versions is one of the most important models of mathematical physics, with applications to different fields [33] as for example in semiconductor electronics [6, 21], nonlinear optics [18], photonics [17], plasma physics [10], fundamentation of quantum mechanics [28], dynamics of accelerators [13], mean-field theory of Bose-Einstein condensates [8, 35] or biomolecule dynamics [9] to cite only a few examples
The range of applicability is large because of the well-known universality of this equation [2]. The study of these equations has served as a catalyzer of the development of new ideas or even mathematical concepts such as solitons [36] or singularities in partial differential equations [31, 15]
In this paper, using Lie symmetries we find general classes of potentials V (x) and nonlinearity functions g(x) for which exact solutions can be constructed by combining solutions of the integrable NLS and solvable potentials V (x)
Summary
The Nonlinear Schrodinger Equation (NLSE) in its many versions is one of the most important models of mathematical physics, with applications to different fields [33] as for example in semiconductor electronics [6, 21], nonlinear optics [18], photonics [17], plasma physics [10], fundamentation of quantum mechanics [28], dynamics of accelerators [13], mean-field theory of Bose-Einstein condensates [8, 35] or biomolecule dynamics [9] to cite only a few examples. Nonlinear Schrodinger equations, Lie symmetries, dynamical systems. We complement that analysis by presenting the general theory, provide more examples, study the case of asymmetric solutions and use qualitative theory of dynamical systems to provide a much more complete analysis of the method and its applications to equations of physical relevance.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
