Showing papers in "Applied Mathematics Letters in 2018"

TL;DR: It is found that the propagation behavior of ShGBs is variable and closely related to the parameter of sinh function (PShF), which is similar to the evolution of temporal higher-order solitons in nonlinear optical fiber.

TL;DR: Using the ψ -Hilfer fractional derivative, this article presented a study of the Hyers-Ulam-Rassias stability of the fractional Volterra integro-differential equation.

TL;DR: Based on the Lax pair of the coupled NLS equation, the determinant representation of the N -fold Darboux transformation(DT) was constructed in this paper, which obtained its higher-order soliton, breather and rogue wave solutions.

TL;DR: By the interaction between lump solution and a pair of resonance stripe solitons, a rogue wave phenomenon is revealed and the result shows that the lump soliton will be drowned or swallowed by the stripe soliton.

TL;DR: The convergence of these methods when the linear system is consistent is proved, and it is shown that these methods can be more efficient than the greedy randomized Kaczmarz method if the relaxation parameter is chosen appropriately.

TL;DR: An analytical study is presented and it is shown that the model has two equilibrium points (disease free equilibrium and endemic equilibrium) and local asymptotic stability is proven for both cases.

TL;DR: The N -fold Darboux transformation (DT) is constructed based on the Lax pair for the Hirota equation and the discrete N -soliton solutions under the vanishing background are derived.

TL;DR: An approach to obtain solutions for the nonlocal nonlinear Schr\"{o}dinger hierarchy from the known ones of the Ablowitz-Kaup-Newell-Segur hierarchy by reduction in terms of double Wronskian is proposed.

TL;DR: Existence and uniqueness of the global positive solution to the stochastic HIV system is proven, and conditions under which extinction and persistence in mean hold, are given.

TL;DR: In this paper, a finite element method using unstructured mesh adapted to the irregular domain is proposed to solve the distributed order space-fractional diffusion equation on an irregular convex domain.

TL;DR: Different height functions of the nonlinear term on special bounded sets together with Leggett–Williams and Krasnosel’skii fixed point theorems are employed to establish the existence of triple positive solutions for a class of higher-order fractional differential equations with integral conditions.

TL;DR: The proposed conformable Swartzendruber models are solved employing the Laplace transform method and validated on the basis of water flow in compacted fine-grained soils.

TL;DR: By constructing a system of dissipative differential inequalities together with a continuity argument, this work provides a sufficient condition for the flocking behavior showing the velocity alignment between particles as time goes to infinity when the maximum value of time delays is sufficiently small.

TL;DR: This letter proposes a class of linear fractional difference equations with discrete-time delay and impulse effects with exact solutions obtained by use of a discrete Mittag-Leffler function withdelay and impulse.

TL;DR: The results show that the extreme behavior of the breather wave yields the rogue wave for the higher-order nonlinear Schrodinger equation.

TL;DR: In this article, the linear superposition principle is applied to the Hirota bilinear form of a new (3+1)-dimensional generalized Kadomtsev-Petviashvili equation, which leads to a sufficient and necessary criterion for the existence of linear subspaces of exponential traveling wave solutions.

TL;DR: A delay-dependent sufficient condition for robust finite-time stability of fractional-order systems with time-varying delay and nonlinear perturbation is established in terms of the Mittag-Leffler function.

TL;DR: This paper establishes excellent conditions to ensure the existence of the twin iterative positive solutions of a class of fractional q -difference Schrodinger equations, but also constructs two convergent monotone explicit iterative schemes to seek them.

TL;DR: The two-component KdV system conjectured to be integrable by Foursov is proved to be both Lax integrability and P-integrable and it is shown that the three two- component Korteweg–de Vries systems are identical under certain invertible linear transformations.

TL;DR: The nonlinear conjugate gradient method is proposed to get the viscoelastic parameters of fractional Maxwell fluid in a rectangular microchannel and combined with the continuity equations and Cauchy momentum equations, the governing equations of velocity distribution are established.

TL;DR: By adding different correction terms, two linearized compact alternating direction implicit (ADI) methods are proposed for solving the two-dimensional nonlinear time fractional Schrodinger equations.

TL;DR: A ( 2 + 1 ) -dimensional Heisenberg ferromagnetic spin chain equation with time-dependent coefficients is investigated, and based on the symbolic computation, Lax pair and infinitely many conservation laws are constructed.

TL;DR: A new merit function is derived, namely the energy gap functional, whose minimum leads to the optimal distribution of source points whose minimum can improve the accuracy of the MFS for solving the mixed boundary value problem as well as the Cauchy problem of the Laplace equation.

TL;DR: Using the fixed point theorem in double cones, it is proved the existence of multiple positive solutions in a system of impulsive integral boundary value problems with sign-changing nonlinearities.

TL;DR: It is established that sufficient conditions for the existence of globally attractive solutions for the Cauchy problems are established, and the characteristics of solutions for fractional differential equations with the Riemann–Liouville derivative are revealed.

TL;DR: A (2+1)-dimensional variable-coefficient nonlinear Schrodinger equation is investigated, which can describe an inhomogeneous Heisenberg ferromagnetic spin chain with the octupole–dipole interaction or alpha helical protein with higher-order excitations and interactions under the continuum approximation.

TL;DR: The multiple exp-function method is utilized for solving the multiple soliton solutions for the new ( 2 + 1 ) -dimensional Korteweg–de Vries equation, which include one-soliton, two-solidon, and three-Soliton type solutions.

TL;DR: A novel approach for detecting unknown boundaries in the two-dimensional anisotropic heat conduction equations based on the boundary function method, in which a partial homogenization function satisfied the over-specified Cauchy data on an arc is derived to effectively solve the inverse geometry problem.

TL;DR: Breather-to-soliton transition is studied for an integrable sixth-order nonlinear Schrodinger equation in an optical fiber and interactions of the breathers and breathers, as well as of thesolitons and solitons, are graphically presented.

TL;DR: Using an equivalence relation to the linear complementarity problem (LCP), two necessary and sufficient conditions for the unique solution of the AVE are presented and some new sufficient conditions are obtained.