On a vector long wave-short wave-type model



报告题目:On a vector long wave-short wave-type model  



腾讯会议:会议 ID523-482-247



报告摘要:A new vector long wave-short wave-type model is proposed by resorting to the zero-curvature equation. Based on the resulting Riccati equations related to the Lax pair and the gauge transformations between the Lax pairs, multifold Darboux transformations are constructed for the vector long wave-short wave-type model. This method is general and is suitable for constructing the Darboux transformations of other soliton equations, especially in the absence of symmetric conditions for Lax pairs. As an illustrative example of the application of the Darboux transformations, exact solutions of the two-component long wave-short wave type model are obtained, including solitons, breathers, and rogue waves of the first, second, third, and fourth orders. All the solutions derived by the Darboux transformations involve square roots of functions, which is not observed in the investigation of other nonlinear integrable equations. This model describes new nonlinear phenomena.


专家简介:耿献国,郑州大学数学与统计学院教授,博士生导师,郑州大学特聘教授。国务院政府特殊津贴专家,2012年获全国百篇优秀博士学位论文指导老师。从事的研究方向是可积系统及应用。曾在Commun. Math. Phys., Trans. Amer. Math. Soc., Adv. Math., J. Nonlinear Sci., SIAM J. Math. Anal., Int. Math. Res. Not. IMRN, Nonlinearity等刊物上发表论文。主持国家自然科学基金重点项目2项和多项国家自然科学基金面上项目等。