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We show that there exists a universal mechanism of long-range solitonattraction in three-dimensional solids and, therefore, of discontinuity of anycommensurate-incommensurate (C-IC) phase transition. This mechanism is due tothe strain dependence of the soliton self-energy and specific features of thesolid-state elasticity. The role of this mechanism is studied in detail for aclass of C-IC transitions where the IC modulation is one-dimensional, theanisotropy in the order parameter space is small, and the symmetry of thesystems allows the existence of the Lifshitz invariant. Two other mechanisms ofsoliton attraction are operative here but the universal mechanism considered inthis paper is found to be the most important one in some cases. Comparison withthe most extensively studied C-IC transition in $\rm K_2SeO_4$ shows that theexperimentally observed thermal anomalies can be understood as a result of thesmearing of the theoretically predicted discontinuous transition.Comment: 8 pages (extended version, title changed

Universal mechanism of discontinuity of commensurate-incommensurate transitions in three-dimensional solids: Strain dependence of soliton self-energy