Abstract
Exact solutions of nonlinear evolution equations are constructed which correspond to a swelling lump which then divides itself into two (or more) solitary waves moving in opposite directions or, conversely, two (or more) solitary waves coming together and annihilating each other with an exponential decay of the amplitude for large times. A particle motion can be associated to the phenomenon.
By now many curious solutions of nonlinear equations are known. We add to this list a class of solutions which correspond to phenomena of the type of pair annihilation, pair production, or cell division. The analysis shows that this class of equations or solutions are very rich.
Lecture given at NATO Advanced Study Institute on Nonlinear Equations in Physics and Mathematics, Istanbul, August 1977.
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References
M. D. Kruskal, Lectures in Appl. Math. 15, Amer. Math. Soc., 61–83 (1974).
F. Calogero, Motion of Poles and Zeros of Special Solutions of Nonlinear and Linear Partial Differential Equations and Related “Solvable” Many-Body Problems, Nuovo Cim. 43B, 177–241 (1978).
F. Calogero, these Proceedings.
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© 1978 D. Reidel Publishing Company, Dordrecht, Holland
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Barut, A.O. (1978). Solutions of Nonlinear Equations Simulating Pair Production and Pair Annihilation. In: Barut, A.O. (eds) Nonlinear Equations in Physics and Mathematics. NATO Advanced Study Institutes Series, vol 40. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-9891-9_3
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DOI: https://doi.org/10.1007/978-94-009-9891-9_3
Publisher Name: Springer, Dordrecht
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