Geodesic
Wave solutions of semilinear parabolic equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 89 (1991) no. 1, pp. 25-47

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Interactions of nonlinear waves (kinks) described by semilinear parabolic equations are investigated. Exact two-phase solutions that generalize Newell's solutions are constructed for nonlinearities having the form of a cubic polynomial. An asymptotic solution describing the interaction of kinks propagating in a strip between the roots of the nonlinearity is obtained for the Kolmogorov–Petrovskii–Piskunov–Fisher equation. 
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     author = {V. G. Danilov and P. Yu. Subochev},
     title = {Wave solutions of semilinear parabolic equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {25--47},
     publisher = {mathdoc},
     volume = {89},
     number = {1},
     year = {1991},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1991_89_1_a3/}
}
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V. G. Danilov; P. Yu. Subochev. Wave solutions of semilinear parabolic equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 89 (1991) no. 1, pp. 25-47. http://geodesic.mathdoc.fr/item/TMF_1991_89_1_a3/