Solitary Wave Solutions of Nonlinear Financial Markets:
Data-Modeling-Concept-Practicing
MA Jin-long and MA Fei-te
© Higher Education Press and Springer-Verlag 2007
Abstract This paper seeks to solve the difficult nonlinear problem in financial markets on the complex system theory and the nonlinear dynamics principle, with the data-model- concept-practice issue-oriented reconstruction of the phase space by the high frequency trade data. In theory, we have achieved the differentiable manifold geometry configuration, discovered the Yang-Mills functional in financial markets, obtained a meaningful conserved quantity through corresponding space-time non-Abel localization gauge symmetry transformation, and derived the financial soliton, which shows that there is a strict symmetry between manifold fiber bundle and gauge field in financial markets. In practical applications of financial markets, we have repeatedly carried out experiments in a fluctuant evolvement, directly simulating and validating the existence of a soliton by researching the price fluctuations (society phenomena) using the same methods and criterion as in natural science and in actual trade to test the stock G-Guangkong and the Fuel Oil futures in China. The results demonstrate that the financial soliton discovered indicates that there is a kind of new substance and form of energy existing in financial trade markets, which likely indicates a new science paradigm in the economy and society domains beyond physics.
Front. Phys. China, 2007, 2(3): 268―374