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  1. No Access

    Article

    Long Time Asymptotics Behavior of the Focusing Nonlinear Kundu-Eckhaus Equation

    The authors study the Cauchy problem for the focusing nonlinear Kundu-Eckhaus (KE for short) equation and construct the long time asymptotic expansion of its solution in fixed space-time cone with C(x1, x2, v1, v

    Ruihong Ma, Engui Fan in Chinese Annals of Mathematics, Series B (2023)

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    Article

    Long Time Asymptotic Behavior for the Nonlocal mKdV Equation in Solitonic Space–Time Regions

    We study the long time asymptotic behavior for the Cauchy problem of an integrable real nonlocal mKdV equation with nonzero initial data in the solitonic regions

    Xuan Zhou, Engui Fan in Mathematical Physics, Analysis and Geometry (2023)

  3. No Access

    Article

    Long-time Asymptotic Behavior for the Derivative Schrödinger Equation with Finite Density Type Initial Data

    In this paper, the authors apply \(\overline \partial \) steepest descent method to study the Cauchy problem for the derivative...

    Yiling Yang, Engui Fan in Chinese Annals of Mathematics, Series B (2022)

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    Article

    Whitham Hierarchy and Generalized Picard–Fuchs Operators in the N=2 Susy Yang–Mills Theory for Classical Gauge Groups

    We derive infinitely many meromorphic differentials based on the fractional powers of the superpotential arising from hyperelliptic curves. We obtain various differential equations expressed in terms of the mo...

    Jialiang Dai, Engui Fan in Theoretical and Mathematical Physics (2019)

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    Article

    The Initial-boundary Value Problem for the Ostrovsky-Vakhnenko Equation on the Half-line

    We analyze an initial-boundary value problem for the Ostrovsky-Vakhnenko equation on the half-line. This equation can be viewed as the short wave model for the Degasperis-Procesi (DP) equation. We show that th...

    Jian Xu, Engui Fan in Mathematical Physics, Analysis and Geometry (2016)

  6. No Access

    Article

    A Riemann-Hilbert approach to the Harry-Dym equation on the line

    In this paper, the authors consider the Harry-Dym equation on the line with decaying initial value. They construct the solution of the Harry-Dym equation via the solution of a 2 × 2 matrix Riemann-Hilbert prob...

    Yu **ao, Engui Fan in Chinese Annals of Mathematics, Series B (2016)

  7. No Access

    Article

    Long-time Asymptotic for the Derivative Nonlinear Schrödinger Equation with Step-like Initial Value

    We study long-time asymptotics of the solution to the Cauchy problem for the Gerdjikov-Ivanov type derivative nonlinear Schrödinger equation ...

    Jian Xu, Engui Fan, Yong Chen in Mathematical Physics, Analysis and Geometry (2013)

  8. No Access

    Article

    Super quasiperiodic wave solutions and asymptotic analysis for \( \mathcal{N} = 1 \) supersymmetric KdV-type equations

    Based on a general multidimensional Riemann theta function and the super Hirota bilinear form, we extend the Hirota method to construct explicit super quasiperiodic (multiperiodic) wave solutions of ...

    Y. C. Hon, Engui Fan in Theoretical and Mathematical Physics (2011)

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    Article

    The algebraic structure of discrete zero curvature equations associated with integrable couplings and application to enlarged Volterra systems

    An algebraic structure of discrete zero curvature equations is established for integrable coupling systems associated with semi-direct sums of Lie algebras. As an application example of this algebraic structur...

    Lin Luo, EnGui Fan in Science in China Series A: Mathematics (2009)