In this paper, we calculate the energy spectrum of interacting gases by converting cluster expansion method in statistical mechanics into a solving eigenvalues. We obtain an explicit expression eigenvalue, which can eigenvalue gas from interparticle potential directly. As example, for with soft-sphere potentials.

in this paper, the bernstein polynomials are used to approximate the solutions of linear integral equations with multiple time lags (iemtl) through expansion methods (collocation method, partition method, galerkin method). the method is discussed in detail and illustrated by solving some numerical examples. comparison between the exact and approximated results obtained from these methods is...

In this paper, using ( ′ G )-expansion method and modified F-expansion method, we give some explicit formulas of exact traveling wave solutions for the (3+1)-dimensional breaking soliton equation. A modified F-expansion method is proposed by taking full advantages of F-expansion method and Riccati equation in seeking exact solutions of the equation. Keywords—Exact solution, The (3+1)-dimensiona...