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Tiecheng Xia

Publications and source records attributed to Tiecheng Xia.

11 recordsLinked to original sources
arXiv2024

Thermal analysis of black hole in de Rham--Gabadadze--Tolley massive gravity in Barrow entropy framework

This study examines a recently hypothesized black hole solution in de Rham--Gabadadze--Tolley massive gravity. Firstly, we consider the negative cosmological constant as a thermodynamic pressure. We extract the thermodynamical properties such as Hawking temperature, heat capacity and Gibbs free energy using the Barrow entropy. We also obtain a new pressure associated to the perfect fluid dark matter and discuss the first-order van der Waals-like phase transition. This black hole's stability is investigated through specific heat and Gibbs free energy. Also, we analyze the thermodynamic curvatures behavior of black hole through geometry methods (Weinhold, Ruppeiner, Hendi-Panahiyah-Eslam-Momennia (HPEM), and geometrothermodynamics (GTD)).

gr-qc↗
arXiv2018

The initial-boundary value problems for the coupled derivative nonlinear Schrödinger equations on the half-line

The unified transform method is used to analyze the initial-boundary value problem for the coupled derivative nonlinear Schrödinger(CDNLS) equations on the half-line. In this paper, we assume that the solution $u(x,t)$ and $v(x,t)$ of CDNLS equations are exists, and we show that it can be expressed in terms of the unique solution of a matrix Riemann-Hilbert problem formulated in the plane of the complex spectral parameter $λ$.

nlin.SI↗
arXiv2017

An initial-boundary value problem for the coupled focusing-defocusing complex short pulse equation with a $4\times4$ Lax pair

In this paper we investigate the coupled focusing-defocusing complex short pulse equation, which describe the propagation of ultra-short optical pulses in cubic nonlinear media. Through the unified transform method, the initial-boundary value problem for the coupled focusing-defocusing complex short pulse equation with $4\times 4$ Lax pair on the half-line are to be analyzed. Assuming that the solution $\{q_1(x,t),q_2(x,t)\}$ of the coupled focusing-defocusing complex short pulse equation exists, we show that $\{q_{1,x}(x,t),q_{2,x}(x,t)\}$ can be expressed in terms of the unique solution of a $4\times 4$ matrix Riemann-Hilbert problem formulated in the complex $λ$-plane. Thus, the solution $\{q_1(x,t),q_2(x,t)\}$ can be obtained by integration with respect to $x$. Moreover, we also get that some spectral functions are not independent and satisfy the so-called global relation.

nlin.SI↗
arXiv2017

A Riemann-Hilbert Approach to the Kundu-Eckhaus Equation on the half-Line

In this paper, we consider the initial-boundary value problem of the Kundu-Eckhaus equation on the half-line by using of the Fokas unified transform method. Assuming that the solution $u(x,t)$ exists, we show that it can be expressed in terms of the unique solution of a matrix Riemann-Hilbert problem formulated in the plane of the complex spectral parameter $λ$. Moreover, we also get there exist spectral functions are not independent and they are satisfying the so-called global relation.

nlin.SI↗
arXiv2017

The coupled Fokas-Lenells equations by a Riemann-Hilbert approach

In this paper, we use the unified transform method to consider the initial-boundary value problem for the coupled Fokas-Lenells equations on the half-line, assuming that the solution $\{q(x,t),r(x,t)\}$ of the coupled Fokas-Lenells equations exists, we show that $\{q_x(x,t),r_x(x,t)\}$ can be expressed in terms of the unique solution of a matrix Riemann-Hilbert problem formulated in the plane of the complex spectral parameter $λ$. Thus, the solution $\{q(x,t),r(x,t)\}$ can be obtained by integration with respect to $x$.

math-ph↗
arXiv2017

Nonlinear integrable couplings of a generalized super Ablowitz-Kaup-Newell-Segur hierarchy and its super bi-Hamiltonian structures

In this paper, a new generalized $5\times5$ matrix spectral problem of Ablowitz-Kaup-Newell-Segur(AKNS) type associated with the enlarged matrix Lie super algebra is proposed and its corresponding super soliton hierarchy is established. The super variational identities is used to furnish super-Hamiltonian structures for the resulting super soliton hierarchy.

math-ph↗
arXiv2017

An integrable generalization of the super Kaup-Newell soliton hierarchy and its bi-Hamiltonian structure

An integrable generalization of the super Kaup-Newell(KN) isospectral problem is introduced and its corresponding generalized super KN soliton hierarchy are established based on a Lie super-algebra B(0,1) and super-trace identity in this paper. And the resulting super soliton hierarchy can be put into a super bi-Hamiltonian form. In addition, a generalized super KN soliton hierarchy with self-consistent sources is also presented.

nlin.SI↗
arXiv2017

The coupled modified nonlinear Schrödinger equations on the half-line via the Fokas method

Coupled modified nonlinear Schrödinger(CMNLS) equations describe the pulse propagation in the picosecond or femtosecond regime of the birefringent optical fibers. In this paper, we use the Fokas method to analyze the initial-boundary value problem for the CMNLS equations on the half-line. Assume that the solution u(x,t) and v(x,t) of CMNLS equations are exists, and we show that it can be expressed in terms of the unique solution of a matrix Riemann-Hilbert problem formulated in the plane of the complex spectral parameter λ.

math-ph↗
arXiv2014

A two-component generalization of Burgers equation with Quasi-periodic solutions

In this paper, we aim for the theta function representation of quasi-periodic solution and related crucial quantities for a two-component generalization of Burgers equation. Our tools include the theory of algebraic curve, the meromorphic function, Baker-Akhiezer functions, the Dubrovin-type equations for auxiliary divisor, with these tools, the explicit representa- tions for above quantities are obtained.

nlin.SI↗
arXiv2014

Algebro-geometric solution of the coupled Burgers equation

We derive theta function representation of algebro-geometric solution of a Coupled Burgers equation which the second nonlinear evolution equation in a hierarchy. We also derive the algebro-geometric characters of the meromorphic function ϕ and the Baker-Akhiezer vector Ψ.

nlin.SI↗