Abstract： In this talk, we propose a systematic approach to find the first integrals and Darboux polynomials of nonlinear differential systems. As applications, some new Darboux polynomials of nonlinear models arising in physics, biology, engineering, and fluid mechanics are investigated by this approach. Particularly, a nonintegrable three-dimensional system with non-chaotic behaviors is introduced and traveling wave solutions of some partial differential equations are presented and classified.

个人简介 （中文）：
冯兆生，美国德克萨斯大学RGV分校Carlos and Stephanie Manrique de Lara讲席教授。主要研究方向是非线性分析，动力系统，数学物理问题，数值计算与模拟等，曾于2015和2021年两次获得德克萨斯大学年度杰出科研成就奖。现任国际知名学术期刊CNSNS的共同主编和EJDE的执行主编，和多个国际SCI杂志的编委及AIMS应用数学系列丛书的编委。

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个人简介 (英文)：

Zhaosheng Feng, Carlos and Stephanie Manrique de Lara Endowed Chair Professor at the School of Mathematical and Statistical Sciences of University of Texas-RGV, USA. He is the recipient of UTRGV Excellence Award in Research/Scholarship/Creative Work in 2015 and 2021. His research interests lie in nonlinear analysis, dynamical systems, computational methods and simulations, mathematical physics, and mathematical biology etc.