Methods of exploration of laser thermonuclear targets by means of computational experiments were elaborated by Kurdyumov (together with academician RAS Alexander Samarskii.
Kurdyumov made an important contribution to the elaboration of fundamental problems of synergetics as well as to the theory of non-linear evolutionary equations.
These results found an important application and experimental confirmation in the problems connected with laser thermonuclear fusion, in experiments on thermochemistry.
From 1983 to 2004 under the direction of the Corresponding Member of the RAS Kurdyumov, and with his immediate assistance, a number of fundamental scientific results in the field of mathematical physics, nonlinear dynamics and synergetics were obtained.
New methods of constructive analysis of solutions of a wide class of non-linear parabolic equations with sources and sinks were developed.
The research results in the field were presented, in particular, in the monograph entitled "Blow-up in quasi-linear parabolic equations", Berlin: Walter de Gruyter, 1995 (in co-authorship with A.
Special attention is drawn to the application of the ideas of synergetics in such fields as strategic planning, analysis of the historical processes, the modelling of educational systems, the philosophical problems of natural sciences.
Laws of Co-evolution of Complex Systems”, Moscow: Nauka Publishers, 1999, are of great interest for the scientific community.