The Theory of Quantum Torus Knots

The mathematical building block presented in the four-volume set is called the theory of quantum torus knots (QTK) a theory that is anchored in the principles of differential geometry and 2D Riemannian manifolds for 3D curved surfaces. The reader is given a mathematical setting from which they will be able to witness the derivations solutions and interrelationships between theories and equations taken from classical and modern physics. Included are the equations of Ginzburg-Landau Gross-Pitaevskii Kortewig-de Vries Landau-Lifshitz nonlinear Schrödinger Schrödinger-Ginzburg-Landau Maxwell Navier-Stokes and Sine-Gordon. They are applied to the fields of aerodynamics electromagnetics hydrodynamics quantum mechanics and superfluidity. These will be utilized to elucidate discussions and examples involving longitudinal and transverse waves convected waves solitons special relativity torus knots and vortices.