关键词: variable coefficient, nonlinear evolution equation, soliton-like solution, truncated expansion method

Abstract: This work is the continuation of the discussion ofRef. [1].In this paper we resolve the equations of isentropic gas dynamics into two problems: the three-dimensional non-constant irrotational flow (thus the isentropic flow, too), and the three-dimensional non-constant indivergentflow (i. e. the in compressible isentropic flow). We apply the theory of functions of a complex variable under Dirac-Pauli representation and the Legendre transformation, transform these equations of two problems from physical space into velocity space, and obtain two general Chaplygm equations in this paper. The general Chaplygin equation is a linear difference equation, and its general solution can be expressed at most by the hypergeometric functions. Thus we can obtain the general solution of general problems for the three-dimensional non-constant isentropic flow of gas dynamics.

Key words: variable coefficient, nonlinear evolution equation, soliton-like solution, truncated expansion method