ON EXACT HYPERGEOMETRIC SOLUTIONS OF CERTAIN SOLITON-LIKE EQUATIONS

It is shown that certain nonlinear wave evolution equations in (1+1)-dimensional space-time in the soliton theory: sine-Gordon (SG), sinh-Gordon (ShG), the nonlinear Schrödinger equation (NLS), the φ⁴ equation in quantum field theory, the Burgers diffusion equation (Brg) and the Huxley equation (Hsl) in biophysics, the Boussinesq equation (Bsq), can be solved in terms of hypergeometric functions of _pF_q-type. Such approach allows to establish the connection between "model" equations and simple functional relations (in the form of diagrams) of these functions; the latter gives the possibility to consider a number of "inverse problems" in the soliton theory in a new way and to get new "models" of solitary waves.