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Symbolic computation of solitons with Macsyma. (English) Zbl 0765.35048
Computational and applied mathematics, II: Differential equations, Sel. Rev. Pap. IMACS 13th World Congr., Dublin/Irel. 1991, 287-296 (1992).
Summary: [For the entire collection see Zbl 0754.00007.]
Hirota’s method for constructing soliton solutions of nonlinear evolution and wave equations is discussed and illustrated. The Macsyma program HIROTA\(\_\)SINGLE automatically calculates \(N\)-soliton solutions for \(N=1,2\) or 3. The program also allows to test the necessary conditions for the existence of four-soliton solutions. Exact analytical solutions of various nonlinear PDEs from soliton theory are presented.

MSC:
35Q51 Soliton equations
68W30 Symbolic computation and algebraic computation
35Q53 KdV equations (Korteweg-de Vries equations)
35Q55 NLS equations (nonlinear Schrödinger equations)
Software:
HIROTA.MAX; MACSYMA
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