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- Title
Long-time asymptotics for the coupled modified complex short-pulse equation.
- Authors
Liu, Wenhao; Geng, Xianguo; Liu, Huan
- Abstract
The Cauchy problem of the coupled modified complex short-pulse equation with decaying boundary conditions $ (x\rightarrow \pm\infty) $ are studied by utilizing the Riemann-Hilbert approach and nonlinear steepest descent method. On the basis of the spectral analysis of $ 4\times 4 $ matrix Lax pair and the inverse scattering transform, the solution to the Cauchy problem is converted to solving a basic Riemann-Hilbert problem. As a special example, the explicit formulas for the one-soliton solutions and breather solutions are given. A model Riemann-Hilbert problem, which can be solved by the parabolic cylindrical functions, is obtained by successive deformation of various corresponding Riemann-Hilbert problems. Finally, the leading order asymptotic behavior of the solution of the Cauchy problem for the coupled modified complex short-pulse equation is derived.
- Subjects
RIEMANN-Hilbert problems; CAUCHY problem; INVERSE scattering transform; EQUATIONS; LAX pair
- Publication
Communications on Pure & Applied Analysis, 2024, Vol 23, Issue 4, p1
- ISSN
1534-0392
- Publication type
Article
- DOI
10.3934/cpaa.2024023