Painlevé-type asymptotics of an extended modified KdV equation in transition regions

DOI10.1016/j.jde.2021.01.020zbMath1475.37077OpenAlexW3125308071MaRDI QIDQ2656280

Nan Liu, Bo-ling Guo

Publication date: 11 March 2021

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2021.01.020

zbMATH Keywords

long-time asymptoticsnonlinear steepest descent methodextended modified KdV equationPainlevé-type functions

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Nonautonomous Hamiltonian dynamical systems (Painlevé equations, etc.) (37J65)

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Uses Software

• rogue-waves

Cites Work

• On the solvability of Painlevé II and IV
• Long time asymptotic behavior of the focusing nonlinear Schrödinger equation
• Soliton resolution for the derivative nonlinear Schrödinger equation
• Extreme superposition: rogue waves of infinite order and the Painlevé-III hierarchy
• Long-time asymptotic behavior for an extended modified Korteweg-de Vries equation
• Asymptotics for the Sasa-Satsuma equation in terms of a modified Painlevé II transcendent
• A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
• The Nonlinear Steepest Descent Method: Asymptotics for Initial-Boundary Value Problems
• Painlevé-Type Asymptotics for the Camassa–Holm Equation
• Asymptotics for the painlevé II equation
• Airy and Painlevé asymptotics for the mKdV equation
• The Gerdjikov‐Ivanov–type derivative nonlinear Schrödinger equation: Long‐time dynamics of nonzero boundary conditions
• Long‐time asymptotics of the nonlinear Schrödinger equation shock problem
• The nonlinear steepest descent method for Riemann-Hilbert problems of low regularity
• The Riemann–Hilbert problem to coupled nonlinear Schrödinger equation: Long-time dynamics on the half-line

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