Construction of solitary wave solutions and rational solutions for the KdV equation by Adomian decomposition method

In this paper, we propose a reliable algorithm to develop exact and approximate solutions for the nonlinear dispersive KdV equation with initial profile. The approach rests mainly on Adomian decomposition method. The single soliton, the two-soliton and rational solutions are obtained by this method. Numerical examples are tested to illustrate the pertinent feature of the proposed algorithm.     

Stationary solutions for the Biswas-Milovic equation

This paper studies the Biswas-Milovic equation by the aid of Lie symmetry analysis. Four types of nonlinearity are being studied for this equation. They are Kerr law, power law, parabolic law and the dual-power law. A closed form stationary solution is obtained for each case.     

A new type of adiabatic invariants for disturbed Birkhoffian system of Herglotz type

The generalized variational principle of Herglotz type provides an effective way to study the problems of conservative and non-conservative systems in a unified way. According to the differential variational principle of Herglotz type, we study the adiabatic invariants for a disturbed Birkhoffian system in this paper. Firstly, the differential equations of motion of the Birkhoffian system based upon this variational principle are given, and the exact invariant of Herglotz type of the system is introduced. Secondly, a new type of adiabatic invariants for the system under the action of small perturbation is obtained. Thirdly, the inverse theorem of adiabatic invariant for the disturbed Birkhoffian system of Herglotz type is obtained. Finally, an example is given.     

Solutions of Two Nonlinear Evolution Equations Using Lie Symmetry and Simplest Equation Methods

In this paper, we study two nonlinear evolution partial differential equations, namely, a modified Camassa–Holm–Degasperis–Procesi equation and the generalized Korteweg–de Vries equation with two power law nonlinearities. For the first time, the Lie symmetry method along with the simplest equation method is used to construct exact solutions for these two equations.     

The non-traveling wave solutions and novel fractal soliton for the (2 + 1)-dimensional Broer–Kaup equations with variable coefficients

A method is proposed by extending the linear traveling wave transformation into the nonlinear transformation with the (G′/G)-expansion method. The non-traveling wave solutions with variable separation can be constructed for the (2 + 1)-dimensional Broer–Kaup equations with variable coefficients via the method. A novel class of fractal soliton, namely, the cross-like fractal soliton is observed by selecting appropriately the arbitrary functions in the solutions.     

Bifurcations of traveling wave solutions for a two-component Fornberg–Whitham equation

A two-component Fornberg–Whitham equation is introduced as a model for water waves. The bifurcations of traveling wave solutions are studied. Parametric conditions to smooth soliton solution, kink solution, antikink solution and uncountable infinite many smooth periodic wave solutions are given. Some expressions for those solutions are presented.     

Self-aggregation of liquids from biomass in aqueous solution

Aggregation of several chemicals from biomass: furfural derived compounds (furfural, 5-methylfurfural, furfuryl alcohol and tetrahydrofurfuryl alcohol), lactate derived compounds (methyl lactate, ethyl lactate and butyl lactate), acrylate derived compound (methyl acrylate) and levulinate compounds (methyl levulinate, ethyl levulinate and butyl levulinate) in aqueous solution has been characterised at T = 298.15 K through density, ρ, speed of sound, u, and isentropic compressibilities, κ_S, measurements. In addition the standard Gibbs free energies of aggregation have been also calculated. Furthermore, in order to deepen insight the behaviour of these chemicals in aqueous solution, the solubility of these compounds has been measured at T = 298.15 K.     

Finite 2-groups in which distinct nonlinear irreducible characters have distinct kernels

In this paper, we study finite 2-groups in which distinct nonlinear irreducible characters have distinct kernels. We prove several results concerning these groups and completely classify 2-groups with at most five nonlinear irreducible characters satisfying this property.     

Density Functional Theory (DFT) modeling and Monte Carlo simulation assessment of inhibition performance of some carbohydrazide Schiff bases for steel corrosion

DFT and Monte Carlo simulation were performed on three Schiff bases namely, 4-(4-bromophenyl)-N^′-(4-methoxybenzylidene)thiazole-2-carbohydrazide (BMTC), 4-(4-bromophenyl)-N^′-(2,4-dimethoxybenzylidene)thiazole-2-carbohydrazide (BDTC), 4-(4-bromophenyl)-N^′-(4-hydroxybenzylidene)thiazole-2-carbohydrazide (BHTC) recently studied as corrosion inhibitor for steel in acid medium. Electronic parameters relevant to their inhibition activity such as E_HOMO, E_LUMO, Energy gap (ΔE), hardness (η), softness ($\sigma$), the absolute electronegativity (χ), proton affinity $\left(\mathrm{PA}\right)$ and nucleophilicity (ω) etc., were computed and discussed. Monte Carlo simulations were applied to search for the most stable configuration and adsorption energies for the interaction of the inhibitors with Fe (110) surface. The theoretical data obtained are in most cases in agreement with experimental results.