A numerical dressing method for the nonlinear superposition of solutions of the KdV equation

作者：Trogdon Thomas^*; Deconinck Bernard

来源：Nonlinearity, 2014, 27(1): 67-86.

DOI：10.1088/0951-7715/27/1/67

• Riemann-Hilbert problems
• Korteweg-de Vries equation
• finite-genus solutions
• Riemann surfaces
• numerical analysis

In this paper we present the unification of two existing numerical methods for the construction of solutions of the Korteweg-de Vries (KdV) equation. The first method is used to solve the Cauchy initial-value problem on the line for rapidly decaying initial data. The second method is used to compute finite-genus solutions of the KdV equation. The combination of these numerical methods allows for the computation of exact solutions that are asymptotically (quasi-)periodic finite-gap solutions and are a nonlinear superposition of dispersive, soliton and (quasi-)periodic solutions in the finite (x, t)-plane. Such solutions are referred to as superposition solutions. We compute these solutions accurately for all values of x and t.

• 出版日期2014-1