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Real, $$p$$-adic and adelic noncommutative scalar solitons. (English) Zbl 1071.35539
Dragovich, B. (ed.) et al., Proceedings of the summer school in modern mathematical physics, Sokobanja, Yugoslavia, August 13–25, 2001. Belgrade: Institute of Physics (ISBN 86-82441-09-8). Sveske Fiz. Nauka, Ser. A, Conf. 3, 283-296 (2002).
The authors successfully demonstrate a new method for obtaining soliton solutions of the basic equation in scalar field theory, $$\phi\star\phi=\phi$$ ($$\star$$ is the Moyal product). Using their method they reobtain the simplest soliton solution in $$2+1$$ single scalar field theory, and other solutions. They also generalize the basic equation in $$p$$-adic case and find corresponding $$p$$-adic and adelic solutions of it.
For the entire collection see [Zbl 1014.00035].
##### MSC:
 35Q51 Soliton equations 53D55 Deformation quantization, star products 81T99 Quantum field theory; related classical field theories