Creation of solitons for sine-Gordon and Korteweg-de Vries equations by means of connections defining the representations of zero curvature. (Russian. English summary) Zbl 1344.35127
Summary: It is possible to create traveling wave type solutions (and in particular soliton solutions) of partial differential equations by means of connections defining the representations of zero curvature. In this paper we create the solitons of the sine-Gordon equation and the Korteweg-de Vries equation. In the final section we compare the proposed method for soliton creation with the inverse scattering method. We systematically use the Cartan-Laptev invariant analytic method in the work.
MSC:
35Q53 | KdV equations (Korteweg-de Vries equations) |
35Q51 | Soliton equations |
35C08 | Soliton solutions |
35C07 | Traveling wave solutions |
37K15 | Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems |
37K35 | Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems |