Darboux Transformations in Integrable Systems: Theory and their Applications to Geometry

By C. Gu, He-sheng Hu, Zixiang Zhou. 2005

307 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Existence of Solitary Waves and Periodic Waves to a Perturbed Generalized KdV Equation (2014, unknown): “There exists a lot of investigation on explicit and exact solitary wave solutions to the KdV equation, for instance, [2,8,9].”
Generalized Darboux transformation and localized waves in coupled Hirota equations (2013, unknown): “+UV − VU = 0. After that, let Φ1 = (ψ1,φ1,χ1)T is a solution of (3) and (4) with u = u[0], v = v[0] and ζ= ζ1, then based on the classical DT of the Ablowitz-Kaup-Newell-Segur (AKNS) spectral problem [16], the following formulas Φ[1] = T[1]Φ,T[1] = ζI − H[0]Λ1H[0]−1, (5) u[1] = u[0] +i(ζ1 −ζ∗ 1) ψ1[”
Consistent Riccati Expansion for Integrable Systems (2015, methodology): “To solve this problem, some elegant approaches have been established such as the inverse scattering transformation [1], Darboux–Bäcklund transformations [2], Hirota’s bilinear direct method [3], and nonlinearizations of Lax pairs [4] have been established.”