Lax pair and vector semi-rational nonautonomous rogue waves for a coupled time-dependent coefficient fourth-order nonlinear Schrödinger system in an inhomogeneous optical fiber<xref rid="cpb_29_3_030202fn1" ref-type="fn">*</xref><fn id="cpb_29_3_030202fn1"><label>*</label><p>Project supported by the BUPT Excellent Ph.D. Students Foundation (Grant No. CX2019201), the National Natural Science Foundation of China (Grant Nos. 11772017 and 11805020), the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), China (Grant No. IPOC: 2017ZZ05), and the Fundamental Research Funds for the Central Universities of China (Grant No. 2011BUPTYB02).</p></fn>

Lax pair and vector semi-rational nonautonomous rogue waves for a coupled time-dependent coefficient fourth-order nonlinear Schrödinger system in an inhomogeneous optical fiber**

Project supported by the BUPT Excellent Ph.D. Students Foundation (Grant No. CX2019201), the National Natural Science Foundation of China (Grant Nos. 11772017 and 11805020), the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), China (Grant No. IPOC: 2017ZZ05), and the Fundamental Research Funds for the Central Universities of China (Grant No. 2011BUPTYB02).

Du Zhong¹, Tian Bo^{1, †}, Qu Qi-Xing², Zhao Xue-Hui¹

The first-order vector semi-rational nonautonomous rogue waves via solutions (9) with N = 1, l₁₁ = 1, l₂₁ = 1, l₃₁ = 1/100, (a1), (a2) μ(t)=t/2, γ(t) = t/50; (b1), (b2) μ(t)=12(t+3) , γ(t)=150(t+3) ; (c1), (c2) μ(t)=12(t+635) , γ(t)=150(t+635) .