ANZIAM 期刊考虑应用数学和相关数学科学的任何领域的论文，旨在以印刷和电子格式快速发表。特别欢迎数学在实际情况中的新应用。所有论文都应包括一些适用性的指示，以及来自整个应用数学界的非专业读者可以理解的介绍。

The ANZIAM Journal welcomes submissions of papers in any area of applied mathematics and related mathematical sciences, aiming for rapid publication in both printed and electronic formats. New applications of mathematics in practical situations are especially encouraged. All papers should include indications of applicability and provide an introduction that is understandable to non-specialist readers from across the applied mathematics community.

ANZIAM Journal 期刊欢迎提交应用数学及相关数学科学领域的论文，旨在快速以印刷和电子格式发表。特别鼓励数学在实际应用中的新探索。所有论文应包含适用性的说明，并提供易于理解的介绍，以便整个应用数学界的非专业读者能够理解。

ANZIAM Journal

Abstract Recently, we analysed spontaneous symmetry breaking (SSB) of solitons in linearly coupled dual-core waveguides with fractional diffraction and cubic nonlinearity. In a practical context, the system can serve as a model for optical waveguides with the fractional diffraction or Bose–Einstein condensate of particles with Lévy index $\alpha &lt;2$ . In an earlier study, the SSB in the fractional coupler was identified as the bifurcation of subcritical type, becoming extremely subcritical in the limit of $\alpha \rightarrow 1$ . There, the moving solitons and collisions between them at low speeds were also explored. In the present paper, we present new numerical results for fast solitons demonstrating restoration of symmetry in post-collision dynamics.

DMITRY V. STRUNIN

BORIS A. MALOMED

JOSHUA L. MCKEIVER

The ANZIAM Journal

SYMMETRY RESTORATION IN COLLISIONS OF SOLITONS IN FRACTIONAL COUPLERS

分数耦合器中孤子碰撞的对称性恢复

Abstract Three-dimensional short-crested water waves are known to host harmonic resonances (HRs). Their existence depends on their sporadicity versus their persistency. Previous studies, using a unique yet hybrid solution, suggested that HRs exhibit sporadic instability, with the domain of instability exhibiting a bubble-like structure which experiences a loss of stability followed by a re-stabilization. Through the calculation of their complete multiple solution structures and normal forms, we discuss the particular harmonic resonance (2,6). The (2,6) resonance was chosen, not only because it is of lower order, and thus more likely to be significant, but also because it is representative of a fully developed three-dimensional water wave field. Its appearance, growth rate and persistency are discussed. On our converged solutions, we show that, at an incidence angle for which HR (2,6) occurs, the associated superharmonic instability is no longer sporadic. It was also found that the multiple solution operates a subcritical pitchfork bifurcation, so regardless of the value of the control parameter, the wave steepness, a stable branch of the solution always exists. As a result, the analysis reveals two competing processes that either provoke and enhance HRs, or inhibit their appearance and development.

SIREL C. COLÓN USECHE

SYLVERT PAUL

MANSOUR IOUALALEN

HARMONIC RESONANCE OF SHORT-CRESTED GRAVITY WAVES ON DEEP WATER: ON THEIR PERSISTENCY

深水短峰重力波的谐振及其持续性

Abstract The study applies a two-dimensional adaptive mesh refinement (AMR) method to estimate the coordinates of the locations of the centre of vortices in steady, incompressible flow around a square cylinder placed within a channel. The AMR method is robust and low cost, and can be applied to any incompressible fluid flow. The considered channel has a blockage ratio of $1/8$ . The AMR is tested on eight cases, considering flows with different Reynolds numbers ( $5\le Re\le 50$ ), and the estimated coordinates of the location of the centres of vortices are reported. For all test cases, the initial coarse meshes are refined four times, and the results are in good agreement with the literature where a very fine mesh was used. Furthermore, this study shows that the AMR method can capture the location of the centre of vortices within the fourth refined cells, and further confirms an improvement in the estimation with more refinements.

R. LAL

Z. LI

FURTHER ACCURACY VERIFICATION OF A 2D ADAPTIVE MESH REFINEMENT METHOD USING STEADY FLOW PAST A SQUARE CYLINDER

方形柱体稳态绕流中二维自适应网格加密方法的进一步精度验证

Abstract Complicated option pricing models attract much attention in financial industries, as they produce relatively better accurate values by taking into account more realistic assumptions such as market liquidity, uncertain volatility and so forth. We propose a new hybrid method to accurately explore the behaviour of the nonlinear pricing model in illiquid markets, which is important in financial risk management. Our method is based on the Newton iteration technique and the Fréchet derivative to linearize the model. The linearized equation is then discretized by a differential quadrature method in space and a quadratic trapezoid rule in time. It is observed through computations that the accurate solutions for the model emerge using very few grid points and time elements, compared with the finite difference method in the literature. Furthermore, this method also helps to avoid consideration of the convergence issues of the Newton approach applied to the nonlinear algebraic system containing many unknowns at each time step if an implicit method is used in time discretization. It is important to note that the Fréchet derivative supports to enhance the convergence order of the proposed iterative scheme.

S. GULEN

M. SARI

AN INVESTIGATION ON NONLINEAR OPTION PRICING BEHAVIOURS THROUGH A NEW FRÉCHET DERIVATIVE-BASED QUADRATURE APPROACH

通过一种基于弗雷歇导数的求积方法对非线性期权定价行为的探究

Abstract We derive and analyse well-posed boundary conditions for the linear shallow water wave equation. The analysis is based on the energy method and it identifies the number, location and form of the boundary conditions so that the initial boundary value problem is well-posed. A finite-volume method is developed based on the summation-by-parts framework with the boundary conditions implemented weakly using penalties. Stability is proven by deriving a discrete energy estimate analogous to the continuous estimate. The continuous and discrete analysis covers all flow regimes. Numerical experiments are presented verifying the analysis.

RUDI PRIHANDOKO

KENNETH DURU

STEPHEN ROBERTS

CHRISTOPHER ZOPPOU

ON WELL-POSED BOUNDARY CONDITIONS AND ENERGY STABLE FINITE-VOLUME METHOD FOR THE LINEAR SHALLOW WATER WAVE EQUATION

关于线性浅水波方程的适定边界条件与能量稳定有限体积法

Abstract The p th ( $p\geq 1$ ) moment exponential stability, almost surely exponential stability and stability in distribution for stochastic McKean–Vlasov equation are derived based on some distribution-dependent Lyapunov function techniques.

Abbreviation	ANZIAM J.
Journal Impact	1.18
Quartiles(Global)	MATHEMATICS, APPLIED(Q3)

ISSN	1446-1811, 1446-8735
h-index	31

Publication Information	Publisher: Cambridge University Press，Publishing cycle: Quarterly，Journal Type: journal，Open Access Journals: No
Basic data	Year of publication: 2000，Proportion of original research papers: 100.00%，Self Citation Rate:0.00%， Gold OA Rate: 25.00%
Average review cycle	网友分享经验：平均1月
Average recruitment ratio	网友分享经验：约25%

ANZIAM Journal

Journal Citation Format

A journal article with 1 author

A journal article with 2 authors

A journal article with 3 authors

A journal article with 5 or more authors

Books Citation Format

Thesis Citation Format

Web sites Citation Format

Patent Citation Format

Staying up late manually editing references? ivySCI automatically matches journals and helps you generate references with a single click.

Share Submission Experience

SYMMETRY RESTORATION IN COLLISIONS OF SOLITONS IN FRACTIONAL COUPLERS

HARMONIC RESONANCE OF SHORT-CRESTED GRAVITY WAVES ON DEEP WATER: ON THEIR PERSISTENCY

FURTHER ACCURACY VERIFICATION OF A 2D ADAPTIVE MESH REFINEMENT METHOD USING STEADY FLOW PAST A SQUARE CYLINDER

AN INVESTIGATION ON NONLINEAR OPTION PRICING BEHAVIOURS THROUGH A NEW FRÉCHET DERIVATIVE-BASED QUADRATURE APPROACH

ON WELL-POSED BOUNDARY CONDITIONS AND ENERGY STABLE FINITE-VOLUME METHOD FOR THE LINEAR SHALLOW WATER WAVE EQUATION

SYMMETRY RESTORATION IN COLLISIONS OF SOLITONS IN FRACTIONAL COUPLERS

HARMONIC RESONANCE OF SHORT-CRESTED GRAVITY WAVES ON DEEP WATER: ON THEIR PERSISTENCY

FURTHER ACCURACY VERIFICATION OF A 2D ADAPTIVE MESH REFINEMENT METHOD USING STEADY FLOW PAST A SQUARE CYLINDER

AN INVESTIGATION ON NONLINEAR OPTION PRICING BEHAVIOURS THROUGH A NEW FRÉCHET DERIVATIVE-BASED QUADRATURE APPROACH

STABILITY ANALYSIS FOR STOCHASTIC MCKEAN–VLASOV EQUATION