A Special Type of Invariant Solutions and its Connection with Dispersion Relations - Ibragimov, Nail H.; Ibragimov, Ranis N. (Discontinuity, Nonlinearity, and Complexity, 2026)
The concept of dispersion relations is widely used in physics and ap- plied mathematics in investigating wave type solutions of differential equations. On the other hand, Lie group analysis provides another useful method for constructing exact solutions of linear and nonlinear differential equations via the concept of invariant solutions. We show in the present paper that for certain types of differential equations there is a remarkable connection between these two concepts. Namely, the idea of dispersion relations leads to a special type of invariant solutions.