Fractal modification of Schrödinger equation and its fractal variational principle
Jian-She Sun
Abstract
With the help of a new fractal derivative, a fractal model for variable coefficients and highly non-linear Schr?dinger equations on a non-smooth boundary are acquired. The variational principles of the fractal variable coefficients and highly non-linear Schr?dinger equations are built successfully by coupling fractal semi-inverse and He?s two-scale transformation methods, which are helpful to reveal the symmetry, to discover the conserved quantity, and the obtained variational principles have widespread applications in numerical simulation.
Topics & Concepts
FractalFractal derivativeVariational principleTransformation (genetics)Schrödinger equationVariable (mathematics)MathematicsInverseBoundary (topology)Mathematical analysisSymmetry (geometry)Applied mathematicsPhysicsFractal analysisFractal dimensionGeometryGeneBiochemistryChemistryFractional Differential Equations SolutionsNeural Networks and ApplicationsMathematical Dynamics and Fractals