Applied Mathematics Letters最新文献

By employing the Hirota method and Wronskian technique, we firstly give the bilinear form, $N$-soliton solutions and the Wronskian solutions of the Hirota–Satsuma equation. Explicit one- and two-soliton solutions are given for the Hirota–Satsuma equation. The solutions of good Boussinesq equation are obtained through the Miura transformation. The two solitons have the degenerated forms of antisoliton-antikink and $W$-shape type.

We present a sequential version of the multilinear Nyström algorithm which is suitable for low-rank Tucker approximation of tensors given in a streaming format. Accessing the tensor $A$ exclusively through random sketches of the original data, the algorithm effectively leverages structures in $A$, such as low-rankness, and linear combinations. We present a deterministic analysis of the algorithm and demonstrate its superior speed and efficiency in numerical experiments including an application in video processing.

We derive the formula for the regularized trace for rank-one perturbations of self-adjoint operators and then justify its applicability to a wide class of differential operators with frozen argument.

In this paper, we study a super Korteweg–de Vries (sKdV) equation proposed by Kupershmidt which possesses a Lax operator with three fully nonlocal terms. The Lax operator is reformulated so that it is of the super constrained modified Kadomtsev–Petviashvili (scmKP) type. By calculating the bi-Hamiltonian structure of the scmKP hierarchy and employing Dirac reduction, we obtain the bi-Hamiltonian structure of the sKdV equation. We also present a spectral problem of its modified system.

In this paper, I prove necessary and sufficient conditions for the existence of Turing instabilities in a general system with three interacting species. Turing instabilities describe situations when a stable steady state of a reaction system (ordinary differential equation) becomes an unstable homogeneous steady state of the corresponding reaction–diffusion system (partial differential equation). Similarly to a well-known inequality condition for Turing instabilities in a system with two species, I find a set of inequality conditions for a system with three species. Furthermore, I distinguish conditions for the Turing instability when spatial perturbations grow steadily and the Turing–Hopf instability when spatial perturbations grow and oscillate in time simultaneously.

In this paper, a spatial sixth-order numerical scheme for solving the time-fractional diffusion equation (TFDE) is proposed. The convergence order of the constructed numerical scheme is $O({\tau }^2+h^6)$, where $\tau$ and $h$ are the temporal and spatial step sizes, respectively. The stability and error estimation of proposed scheme are given by using Fourier method. Some numerical examples are studied to demonstrate the correctness and effectiveness of the scheme and validate the theoretical analysis.

We continue our effort in Li et al. (2024) to explore an interpolated coefficients stabilizer-free weak Galerkin finite element method (IC SFWG-FEM) to solve a one-dimensional semilinear parabolic convection–diffusion equation. Due to the introduction of interpolated coefficients and the design without stabilizers, this method not only possesses the capability of approximating functions and sparsity in the stiffness matrix, but also reduces the complexity of analysis and programming. Theoretical analysis of stability for the semi-discrete IC SFWG finite element scheme is provided. Moreover, numerical experiments are carried out to demonstrate the effectivity and stability.

As a typical representative of viscoelastic fluids, second-grade fluids have many applications, such as paints, food products, and cosmetics. In this paper, the equation for describing the fractional second-grade fluid with the power-law viscosity on a semi-infinite plate under the influence of a magnetic field is studied. The numerical solution is obtained using the finite difference method. To handle the semi-unbounded region, the (inverse) $z$-transform is applied to establish the absorbing boundary condition (ABC) for the solution at the cut-off point. In addition, the numerical example analyzes the superiority of the ABC over the directly truncated boundary condition and the effects of different parameters on the velocity distribution. The conclusion is that the slip parameter, power-law exponent parameter, and power-law index parameter promote the fluid flow, while the magnetic field and fractional parameter hinder the fluid flow.

This paper deals with a damped shear beam model studied in Júnior et al. 2021. By using the theory of $C_0$-semigroup, the results on well-posedness were improved.

The crossing curves method, which allows delays to vary simultaneously, is generalized to the scenario that four terms exist in the characteristic equations with delay-dependent coefficients. The crossing curves on the two-delay parameter plane are first plotted by our generalized algorithms. The criteria to determine the crossing direction are also given. Finally, an example is provided to support our method and illustrate its fortes.