Soliton solutions to the KdV equation and supersymmetric quantum mechanics
Professor Fung, Peter Chin Wan (Principal investigator)
Dr Lee (Co-Investigator)
Dr Kong (Co-Investigator)
Professor Cheng (Co-Investigator)
Other Funding Scheme
Solutions to the (classical) KdV equations are potentials of the Schrodinger equation in quantum mechanics. Time evolutions of the KdV solutions represent 'isospectral flows' of the Schrodinger hamiltonian. A system of transformations has been developed by which isospectral hamiltonians can be produced via the 'inverse scattering' method (which is one of the two most powerful methods in finding solutions to nonlinear equations). The stated transformations are related to supersymmetric quantum mechanics recently developed by others a few years ago. The main aim is to gain insight into the possibility of using soliton physics to interpret or reformulate quantum theory.