Geodesic
Generalized conditional symmetries and exact solutions of non-integrable equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 99 (1994) no. 2, pp. 263-277

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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. 
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     author = {A. S. Fokas and Q. M. Liu},
     title = {Generalized conditional symmetries and exact solutions of non-integrable equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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A. S. Fokas; Q. M. Liu. Generalized conditional symmetries and exact solutions of non-integrable equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 99 (1994) no. 2, pp. 263-277. http://geodesic.mathdoc.fr/item/TMF_1994_99_2_a12/