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Asymptotics of solutions to a fifth-order modified Korteweg-de Vries equation in the quarter plane. (English) Zbl 1479.35744

Summary: The large-time behavior of solutions to a fifth-order modified Korteweg-de Vries equation in the quarter plane is established. Our approach uses the unified transform method of A. S. Fokas [Commun. Math. Phys. 230, No. 1, 1–39 (2002; Zbl 1010.35089)] and the nonlinear steepest descent method of P. Deift and X. Zhou [Ann. Math. (2) 137, No. 2, 295–368 (1993; Zbl 0771.35042)].

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35Q15 Riemann-Hilbert problems in context of PDEs
35G31 Initial-boundary value problems for nonlinear higher-order PDEs
35B40 Asymptotic behavior of solutions to PDEs
37K15 Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems

Software:

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References:

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