%0 Journal Article %1 0253-6102-61-4-03 %A Ying-Ying, Sun %A Juan-Ming, Yuan %A Da-Jun, Zhang %D 2014 %J Communications in Theoretical Physics %K complex %N 4 %P 415 %T Solutions to the Complex Korteweg-de Vries Equation: Blow-up Solutions and Non-Singular Solutions %U http://stacks.iop.org/0253-6102/61/i=4/a=03 %V 61 %X 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.

@article{0253-6102-61-4-03, 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.}, added-at = {2014-06-26T14:39:21.000+0200}, author = {Ying-Ying, Sun and Juan-Ming, Yuan and Da-Jun, Zhang}, biburl = {https://www.bibsonomy.org/bibtex/2a18e5ab883522c9ea4c385df459e3a6d/docal}, description = {Solutions to the Complex Korteweg-de Vries Equation: Blow-up Solutions and Non-Singular Solutions - Abstract - Communications in Theoretical Physics - IOPscience}, interhash = {8873311853bbf0d136b49207a0403aa3}, intrahash = {a18e5ab883522c9ea4c385df459e3a6d}, journal = {Communications in Theoretical Physics}, keywords = {complex}, number = 4, pages = 415, timestamp = {2014-06-26T14:39:21.000+0200}, title = {Solutions to the Complex Korteweg-de Vries Equation: Blow-up Solutions and Non-Singular Solutions}, url = {http://stacks.iop.org/0253-6102/61/i=4/a=03}, volume = 61, year = 2014 }