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Gui Mu

Publications and source records attributed to Gui Mu.

5 recordsLinked to original sources
arXiv2025

Rogue wave patterns associated with Adler Moser polynomials in the nonlocal nonlinear Schr\"odinger equation

In this paper, novel rogue wave patterns in the nolocal nonlinear Schr\"odinger equation (NLS) are investigated by means of asymptotic analysis, including heart-pentagon, oval-trangle, and fan-trangle. It is demonstrated that when multiple free parameters get considerably large, rogue wave patterns can approximately be predicted by the root structures of Adler-Moser polynomials. These polynomials, which extend the Yablonskii-Vorob'ev polynomial hierarchy, exhibit richer geometric shapes in their root distributions. The (x,t)-plane is partitioned into three regions and through a combination of asymptotic results in different regions, unreported rogue wave patterns can be probed. Predicted solutions are compared with true rogue waves in light of graphical illustrations and numerical confirmation, which reveal excellent agreement between them.

nlin.PS↗
arXiv2023

General Rational Solutions and Soliton Solutions of the Nonlocal Resonant Nonlinear Schrodinger Equations

General rational solutions for the nonlocal resonant nonlinear Schrodinger equations are derived by using the Hirota bilinear method and the KP hierarchy reduction method. These rational solutions are presented in terms of determinants in which the elements are algebraic expressions. A weaker condition is given for KP reduction in the nonlocal case. The dynamics of first-order solutions are investigated in details. As a special case, we studied rantional solutions of the RNLS equation. Moreover, soliton solutions of the RNLS equation are given by using the Backlund transformation and nonlinear superposition formula.

nlin.SI↗
arXiv2020

The proof of Gromoll-Walschap conjecture

It is conjectured that there are no Riemannian foliations on compact manifold of negative curvature by Gromoll-Walschap in \cite{DG}. In this note we give a positive answer.

math.DG↗
arXiv2014

Dynamics of rogue waves on a multi-soliton background in a vector nonlinear Schrodinger equation

General higher order rogue waves of a vector nonlinear Schrodinger equation (Manakov system) are derived using a Darboux-dressing transformation with an asymptotic expansion method. The Nth order semi-rational solutions containing 3N free parameters are expressed in separation of variables form. These solutions exhibit rogue waves on a multisoliton background. They demonstrate that the structure of rogue waves in this two-component system is richer than that in a one-component system. The study of our results would be of much importance in understanding and predicting rogue wave phenomena arising in nonlinear and complex systems, including optics, fluid dynamics, Bose-Einstein condensates and finance and so on.

nlin.SI↗