The solvability of some exactly solvable soliton-like equations in terms of hypergeometric functions

It is shown that some nonlinear wave evolution equations in $1+1$-dimensional space-time in the soliton theory can be solved in terms of hypergepmetric 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.