Showing papers in "Applied Mathematics Letters in 2019"

TL;DR: This paper suggests an easier approach by the Laplace transform to determining the multiplier, making the method accessible to researchers facing various nonlinear problems.

TL;DR: Symbolic computation on an observationally/experimentally-supported (2+1)-dimensional generalized variable-coefficient Kadomtsev-Petviashvili-Burgers-type equation is done, for certain dusty plasmas, relying on such plasma coefficient functions as the nonlinearity, dispersion, dusty-fluid-viscosity-dissipation, geometric-effect and diffraction/transverse-perturbation coefficients.

TL;DR: The sufficient conditions for existence and uniqueness of solutions and δ -Ulam–Hyers–Rassias stability of an impulsive fractional differential equation involving ψ -Hilfer fractional derivative are investigated.

TL;DR: A generalized AB system, which is used to describe certain baroclinic instability processes in the geophysical flows, is investigated, and the Darboux and generalizedDarboux transformations are derived, both relevant to the coefficient of the nonlinear term and coefficient related to the shear.

TL;DR: Based on the robust inverse scattering method, the high-order rogue wave of generalized nonlinear Schrodinger equation with nonzero boundary is given using the elementary Darboux transformation but not with the limit progress, which is more convenient than before.

TL;DR: A localized version of the MFS (LMFS), based on the “global” boundary discretization, is proposed for the large-scale modeling of two-dimensional (2D) elasticity problems and yields a sparse and banded matrix system which makes the method very attractive for large- scale simulations.

TL;DR: The non-negativity and the boundedness of solutions are studied, the global asymptotic stability of disease free equilibrium is investigated and the basic reproduction number R 0 is calculated.

TL;DR: The bilinear method is employed to construct the multiple lump solutions of the (3+1)-dimensional potential Yu–Toda–Sasa–Fukuyama equation in fluid dynamics, and the 1-lump solutions, 3-lumping solutions and 6-lumped solutions are explicitly presented.

TL;DR: In this article, it was shown that the Kolmogorov N -width d N (M) is the limit of the worst-case error for the hyperbolic wave equation with discontinuous initial conditions.

TL;DR: Using Hirota bilinear method, four kinds of localized waves, solitons, breathers, lumps and rogue waves of the extended (3+1)-dimensional Jimbo–Miwa equation are constructed.

TL;DR: Using the asymmetric method, the analytic one-soliton solution of the CCQGLE is obtained for the first time and it is shown that the transmission of the soliton is controlled by changing the values of related parameters.

TL;DR: A generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev–Petviashvili equation, which describes the propagation of nonlinear waves in fluid dynamics, is investigated and it is shown that the one-periodic wave solutions approach theOne-soliton solutions when the amplitude η → 0.

TL;DR: By applying the method of moving planes, the results for the non-existence and radial symmetry of solution for a nonlinear Schrodinger equation involving the fractional Laplacian and Hardy potential are established.

TL;DR: The existence theorem and asymptotic properties of radial positive solutions are established by using a new renormalization technique.

TL;DR: A robust kernel-based collocation method for solving multi-term variable-order time fractional partial differential equations (VOTFPDEs), which avoids troublesome mesh generation for high-dimensional problems involving irregular geometries.

TL;DR: This paper makes a first attempt to investigate the long-time behaviour of solutions of 2D acoustic wave equation by integrating strengths of the Krylov deferred correction method in temporal direction and the meshless generalized finite difference method (GFDM) in space domain.

TL;DR: The focus is put in the effect of this kind of fractional derivatives in the search of roots of nonlinear equations and its dependence on the initial estimations.

TL;DR: It is proved that the nonlinear stochastic SIS epidemic system with multiplicative noise generates a random dynamical system which has a tempered compact random absorbing set, implying the condition for the extinction of the disease.

TL;DR: In this paper, the inverse coefficients problem for a quasilinear elliptic equation of divergence form ∇ ⋅ C → ( x, ∇ u ( x ) ) = 0, in a bounded smooth domain Ω, was considered.

TL;DR: A novel class of arbitrarily high-order and unconditionally energy-stable algorithms for gradient flow models by combining the energy quadratization technique and a specific class of Runge–Kutta methods, which is named the EQRK schemes are presented.

TL;DR: This work theoretically investigate the evolution of the soliton pairs in strongly nonlocal nonlinear media, which is modeled by the non local nonlinear Schrodinger equation, and demonstrates that the motion state of thesoliton pairs is mirror-symmetry.

TL;DR: An error estimate has been proposed to find a second-order finite difference scheme for solving the Riesz space distributed-order diffusion equation and the numerical results show the efficiency of the new technique.

TL;DR: The unconditional energy stability for a class of gradient flows and their semi-discrete schemes is proved carefully and rigorously and all nonlinear terms can be treated semi-explicitly.

TL;DR: Numerical results show that the proposed algorithm is feasible and has faster convergence rate than the greedy randomized Kaczmarz algorithm.

TL;DR: Variable separation exponential-form solution of (1+1)-dimensional coupled integrable dispersionless equations in physics and mathematics is obtained via the projective Riccati equation method and the singularity structure without the physical meaning is found for the original components of the system.

TL;DR: It is shown that fission and fusion interactions occur in the lump-kink solutions of the Boiti–Leon–Manna–Pempinelli (BLMP) equation.

TL;DR: By using critical point theory, some sufficient conditions on the existence of infinitely many positive solutions of the boundary value problems for a second-order ϕ c -Laplacian difference equation are obtained.

TL;DR: By constructing the Darboux transformation of nonlocal FL equation, its different kinds of exact solutions including bright/dark solitons, kink solutions, periodic solutions and several types of mixed soliton solutions are obtained.

TL;DR: Some novel non-autonomous soliton solutions of nonlocal GP equation are derived via inverse scattering and similarity transformations, which can present the potential applications to the soliton wave phenomena in nonlocal wave models.

TL;DR: It is proved that the backward problem for a time–space fractional diffusion with nonlinear source is ill-posed in the sense of Hadamard and the convergence rate for the regularized solution can be proved.