| Abstract: | We introduce the concept of a generalized conditional symmetry. This concept provides an algorithm for constructing physically important exact solutions of non-integrable equations. Examples include 2-shock and 2-soliton solutions. The existence of such exact solutions for non-integrable equations can be traced back to the relation of these equations with integrable ones. In this sense these exact solutions are remnants of integrability.Department of Mathematics and Computer Science and Institute for Nonlinear Studies, Clarkson University, Potsdam, New York 13699-5815. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 99, No. 2, pp. 263–277, May, 1994. |
