非线性方程孤子-混沌双解的物理意义,泛量子理论和非线性数学的某些应用

Physical meaning of double solutions with chaos-soliton in nonlinear equations,the extensivequantum theory and some applications on nonlinear mathematics

某些非线性方程中存在混沌-孤子双解,其具有波粒二象性等物理意义.然后探讨了孤子的量子理论,一方面发展孤子理论为量子化的;另一方面用孤子方法量子化.量子孤子化就对应泛量子理论.最后讨论非线性数学的某些应用.非线性数学是演化、相变等必不可少的条件.数学和物理、化学、天文、生物等的非线性应该共同发展.

The double solutions with chaos and soliton exist in some nonlinear equations,whose physical meaning is the wave-particle duality,etc.Then the quantum theory of soliton is researched.For one thing the soliton theory is developed to quantization,for another the quantization is used by the soliton method.The quantized soliton just corresponds to the extensive quantum theory.Finally,some applications on nonlinear mathematics are discussed.The nonlinear mathematics is a necessary condition for the evolvement and phase transition,etc.The nonlinearity of mathematics and physics,chemistry,astronomy,biology and so on should be together developed.