Generalized conditional symmetries and exact solutions of non-integrable equations. (English) Zbl 0850.35097

Theor. Math. Phys. 99, No. 2, 571-582 (1994) and Teor. Mat. Fiz. 99. No. 2, 263-277 (1994).
Summary: 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.


35Q53 KdV equations (Korteweg-de Vries equations)
35L67 Shocks and singularities for hyperbolic equations
35Q51 Soliton equations
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