Related papers: ILW equation for the Hodge integrals revisited
This paper focuses on the modulation instability, conservation laws and localized wave solutions of the generalized coupled Fokas-Lenells equation. Based on the theory of linear stability analysis, distribution pattern of modulation…
We develop wavelet representations for edge-flows on simplicial complexes, using ideas rooted in combinatorial Hodge theory and spectral graph wavelets. We first show that the Hodge Laplacian can be used in lieu of the graph Laplacian to…
We prove a compactness result for holomorphic curves with boundary on an immersed Lagrangian submanifold with clean self-intersection. As a consequence, we show that the number of intersections of such holomorphic curves with the…
In an interesting recent analysis, Haragus-Johnson-Perkins-de Rijk have shown modulational stability under localized perturbations of steady periodic solutions of the Lugiato-Lefever equation (LLE), in the process pointing out a difficulty…
A closed formula is obtained for the integral $\int_{\mathcal{\bar{H}}_g^1}\kappa_{1}\psi^{2g-2}$ of tautological classes over the locus of hyperelliptic Weierstra\ss{} points in the moduli space of curves. As a corollary, a relation…
In this paper we provide a short new proof for the integrality of Rothblum's linear description of the convex hull of incidence vectors of stable matchings in bipartite graphs. In the spirit of iterative rounding proofs, the key feature of…
The algebraic Hodge theorem was proved in a beautiful 1987 paper by Deligne and Illusie, using positive characteristic methods. We argue that the central algebraic object of their proof can be understood geometrically as a line bundle on a…
A moduli space of stable maps to the fibers of a fiber bundle is constructed. The new moduli space is a family version of the classical moduli space of stable maps to a non-singular complex projective variety. The virtual cycle for this…
We derive the precise stability criterion for smooth solitary waves in the b-family of Camassa-Holm equations. The smooth solitary waves exist on the constant background. In the integrable cases b = 2 and b = 3, we show analytically that…
This paper investigates the identification of two coefficients in a coupled hyperbolic system with an observation on one component of the solution. Based on the the Carleman estimate for coupled wave equations a logarithmic type stability…
The Hamiltonian theory of isomonodromy equations for meromorphic connections with irregular singularities on algebraic curves is constructed. An explicit formula for the symplectic structure on the space of monodromy and Stokes matrices is…
In this note, we use the method of [3] to give a simple proof of famous Witten conjecture. Combining the coefficients derived in our note and this method, we can derive more recursion formulas of Hodge integrals.
We establish an explicit formula for the Half-Wave maps equation for rational functions with simple poles. The Lax pair provides a description of the evolution of the poles. By considering a half-spin formulation, we use linear algebra to…
We prove up to the boundary regularity estimates in Morrey-Lorentz spaces for weak solutions of the linear system of differential forms with regular anisotropic coefficients \begin{equation*} d^{\ast} \left( A d\omega \right) +…
In this paper, it is proved that the KdV-Burgers equation with a monostable source term of Fisher-KPP type has small-amplitude periodic traveling wave solutions with finite fundamental period. These solutions emerge from a subcritical local…
Following the work of Gangl, Goncharov and Levin in [GGL], we will give a combinatorial framework for motivic study of iterated integrals on the affine line. We will show that under a certain genericity condition these combinatorial objects…
In this paper we study the problem of explicitly describing the space of invariant linear forms on induced distinguished representations in terms of invariant linear forms on the inducing representation. More precisely, for certain tempered…
In recent years the topic of localized wave solutions of the homogeneous scalar wave equation, i.e., the wave fields that propagate without any appreciable spread or drop in intensity, has been discussed in many aspects in numerous…
This work presents a space-time isogeometric analysis of biharmonic wave problem, in contrast to the more common application of space-time methods to second order wave equations. We first establish the unique solvability of the continuous…
We prove some combinatorial results related to a formula on Hodge integrals conjectured by Mari\~no and Vafa. These results play important roles in the proof and applications of this formula by the author jointly with Chiu-Chu Melissa Liu…