التفاصيل البيبلوغرافية
| العنوان: |
Long-time asymptotics for the coupled modified complex short-pulse equation. |
| المؤلفون: |
Liu, Wenhao, Geng, Xianguo, Liu, Huan |
| المصدر: |
Communications on Pure & Applied Analysis; Apr2024, Vol. 23 Issue 4, p1-39, 39p |
| مصطلحات موضوعية: |
RIEMANN-Hilbert problems, CAUCHY problem, INVERSE scattering transform, EQUATIONS, LAX pair |
| مستخلص: |
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. [ABSTRACT FROM AUTHOR] |
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| قاعدة البيانات: |
Complementary Index |
