English

Solutions to the complex Korteweg-de Vries equation: Blow-up solutions and non-singular solutions

Exactly Solvable and Integrable Systems 2015-06-15 v1 Analysis of PDEs

Abstract

In the paper two kinds of solutions are derived for the complex Korteweg-de Vries equation, including blow-up solutions and non-singular solutions. We derive blow-up solutions from known 1-soliton solution and a double-pole solution. There is a complex Miura transformation between the complex Korteweg-de Vries equation and a modified Korteweg-de Vries equation. Using the transformation, solitons, breathers and rational solutions to the complex Korteweg-de Vries equation are obtained from those of the modified Korteweg-de Vries equation. Dynamics of the obtained solutions are illustrated.

Keywords

Cite

@article{arxiv.1305.3076,
  title  = {Solutions to the complex Korteweg-de Vries equation: Blow-up solutions and non-singular solutions},
  author = {Ying-ying Sun and Juan-ming Yuan and Da-jun Zhang},
  journal= {arXiv preprint arXiv:1305.3076},
  year   = {2015}
}

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