A Riemann–Hilbert approach for the modified short pulse equation

ABSTRACT

We present a Riemann–Hilbert approach for the modified short pulse equation $$\begin{array}{c}\hfill q_{\mathit{xt}}=q+\frac{1}{2}q{(q^2)}_{\mathit{xx}}\end{array}$$

on the line. This approach allows us to give a representation of the solution to the Cauchy problem, which can be efficiently used in studying its long-time behavior, also to describe the soliton solutions.

KEYWORDS:

• Modified short pulse equation
• Riemann–Hilbert problem
• long-time asymptotics
• soliton solutions

AMS SUBJECT CLASSIFICATIONS:

• 35Q15
• 35G25

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China [grant number 11731014], [grant number 11471099].