Unexpected configurations for the optical solitons propagation in lossy fiber system with dispersion terms effect

In this work, we will design unexpected configurations for the optical soliton propagation in lossy fiber system in presence the dispersion term solitons via two distinct and impressive techniques. The first one is the (G’/G)-expansion method, while the second is solitary wave ansatze method. The two methods are implemented in same vein and parallel. The obtained perceptions are new and weren’t achieved before. The comparison between our achieved visions and that achieved by other authors who used different schemas has been documented.

Improvement of the Gaussian Electrostatic Model by Separate Fitting of Coulomb and Exchange-Repulsion Densities and Implementation of a new Dispersion term

The description of each separable contribution of the intermolecular interaction is a useful approach to develop polarizable force fields (polFF). The Gaussian Electrostatic Model (GEM) is based on this approach, coupled with the use of density fitting techniques. In this work, we present the implementation and testing of two improvements of GEM: the Coulomb and Exchange-Repulsion energies are now computed with separate frozen molecular densities, and a new dispersion formulation inspired by the SIBFA polFF, which has been implemented to describe the dispersion and charge–transfer interactions. Thanks to the combination of GEM characteristics and these new features, we demonstrate a better agreement of the computed structural and condensed properties for water with experimental results, as well as binding energies in the gas phase with the ab initio reference compared with the previous GEM* potential. This work provides further improvements to GEM and the items that remain to be improved, and the importance of the accurate reproduction for each separate contribution.

Dynamic Behaviors of Soliton Solutions for a Three-Coupled Lakshmanan-Porsezian-Daniel Model

In this paper, we use the Riemann-Hilbert (RH) approach to examine the integrable three-coupled Lakshmanan-Porsezian-Daniel (LPD) model, which describe the dynamics of alpha helical protein with the interspine coupling at the fourth-order dispersion term. Through the spectral analysis of Lax pair, we construct the higher order matrix RH problem for the three-coupled LPD model, when the jump matrix of this particular RH problem is a 4×4 unit matrix, the exact N-soliton solutions of the three-coupled LPD model can be exhibited. As special examples, we also investigate the nonlinear dynamical behaviors of the single-soliton, two-soliton, three-soliton and breather soliton solutions. Finally, an integrable generalized N-component LPD model with its linear spectral problem is discussed.

Modeling viscoacoustic wave propagation using a new spatial variable-order fractional Laplacian wave equation

We propose a new time-domain viscoacoustic wave equation for simulating wave propagation in anelastic media. The new wave equation is derived by inserting the complex-valued phase velocity described by the Kjartansson attenuation model into the frequency-wavenumber domain acoustic wave equation. Our wave equation includes one second-order temporal derivative and two spatial variable-order fractional Laplacian operators. The two fractional Laplacian operators describe the phase dispersion and amplitude attenuation effects, respectively. To facilitate the numerical solution for the proposed wave equation, we use the arbitrary-order Taylor series expansion (TSE) to approximate the mixed domain fractional Laplacians and achieve the decoupling of the wavenumber and the fractional order. Then the proposed viscoacoustic wave equation can be directly solved using the pseudospectral method (PSM). We adopt a hybrid pseudospectral/finite-difference method (HPSFDM) to stably simulate wave propagation in arbitrarily complex media. We validate the high accuracy of the proposed approximate dispersion term and approximate dissipation term in comparison with the accurate dispersion term and accurate dissipation term. The accuracy of numerical solutions is evaluated by comparison with the analytical solutions in homogeneous media. Theory analysis and simulation results show that our viscoacoustic wave equation has higher precision than the traditional fractional viscoacoustic wave equation in describing constant- Q attenuation. For a model with Q < 10, the calculation cost for solving the new wave equation with TSE HPSFDM is lower than that for solving the traditional fractional-order wave equation with TSE HPSFDM under the high numerical simulation precision. Furthermore, we demonstrate the accuracy of HPSFDM in heterogeneous media by several numerical examples.

Blow-Up of Solutions for a Class Quasilinear Wave Equation with Nonlinearity Variable Exponents

This work deals with the blow-up of solutions for a new class of quasilinear wave equation with variable exponent nonlinearities. To clarify more, we prove in the presence of dispersion term − Δ u t t a finite-time blow-up result for the solutions with negative initial energy and also for certain solutions with positive energy. Our results are extension of the recent work (Appl Anal. 2017; 96(9): 1509-1515).

A new (3 + 1)-dimensional Painlevé-integrable Sakovich equation: multiple soliton solutions

Purpose This paper aims to develop a new (3 + 1)-dimensional Painlev´e-integrable extended Sakovich equation. This paper formally derives multiple soliton solutions for this developed model. Design/methodology/approach This paper uses the simplified Hirota’s method for deriving multiple soliton solutions. Findings This paper finds that the developed (3 + 1)-dimensional Sakovich model exhibits complete integrability in analogy with the standard Sakovich equation. Research limitations/implications This paper addresses the integrability features of this model via using the Painlev´e analysis. This paper reports multiple soliton solutions for this equation by using the simplified Hirota’s method. Practical implications The study reports three non-linear terms added to the standard Sakovich equation. Social implications The study presents useful algorithms for constructing new integrable equations and for handling these equations. Originality/value The paper reports a new Painlev´e-integrable extended Sakovich equation, which belongs to second-order partial differential equations. The constructed model does not contain any dispersion term such as uxxx.

Blow-up phenomena for the sixth-order Boussinesq equation with fourth-order dispersion term and nonlinear source

<p style='text-indent:20px;'>This paper deals with the sixth-order Boussinesq equation with fourth-order dispersion term and nonlinear source. By using some ordinary differential inequalities, the conditions on finite time blow-up of solutions are given with suitable assumptions on initial values. Moreover, the upper and lower bounds of the blow-up time are also investigated.</p>