Abstract:
In the presented paper, in the case of a homogeneous medium, the dualism of spaces of soliton solutions and solutions of an induced point-type functional differential equation is described, and existence and uniqueness theorems for such dual solutions are formulated. Such dualism refers to a number of dualisms of various mathematical objects and, in particular, such as a topological linear space and its conjugate space. In the case of an inhomogeneous medium, a different type of dualism is described for spaces of quasi-soliton solutions and solutions of an induced one-parameter family of a point-type functional differential equation, and existence and uniqueness theorems for such dual solutions are formulated. The entire family of soliton (in the case of a homogeneous medium) and quasi-soliton (in the case of an inhomogeneous medium) solutions is constructed for the finite-difference analog of the wave equation with a nonlinear potential.
