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.
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) |
