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Long-time asymptotic for the Hirota equation via nonlinear steepest descent method

Institution:	1. School of Mathematical Sciences, Fudan University, Shanghai 200433, PR China;2. College of Science, University of Shanghai for Science and Technology, Shanghai 200093, PR China;1. College of Science, University of Shanghai for Science and Technology, Shanghai 200093, People''s Republic of China;2. School of Mathematical Sciences, Institute of Mathematics and Key Laboratory of Mathematics for Nonlinear Science, Fudan University, Shanghai 200433, People''s Republic of China;3. Department of Mathematics, University of Macau, Macau, People''s Republic of China;1. Institute of Applied Physics and Computational Mathematics, Beijing 100088, PR China;2. The Graduate School of China Academy of Engineering Physics, Beijing 100088, PR China;3. College of Science, Minzu University of China, Beijing 100081, PR China

Abstract:	We present the Riemann–Hilbert problem formalism for the initial value problem for the Hirota equation on the line. We show that the solution of this initial value problem can be obtained from that of associated Riemann–Hilbert problem, which allows us to use nonlinear steepest descent method/Deift–Zhou method to analyze the long-time asymptotic for the Hirota equation.

Keywords:	Hirota equation Long-time asymptotic Nonlinear steepest descent method
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