Travelling wave solutions for the generalized Schrödinger equation

In this work, the generalized nonlinear Schrödinger equation is investigated. This equation is integrable and admits Lax pair. To obtain travelling wave solutions the extended tanh method is applied. This method is effective to obtain the exact solutions for different types of nonlinear partial differential equations. Graphs of obtained solutions are presented. The derived solutions are found to be important for the explanation of some practical physical problems.

Lagrangian Formulation, Conservation Laws, Travelling Wave Solutions: A Generalized Benney-Luke Equation

The aim of this paper is to find the Noether symmetries of a generalized Benney-Luke equation. Thereafter, we construct the associated conserved vectors. In addition, we search for exact solutions for the generalized Benney-Luke equation through the extended tanh method. A brief observation on equations arising from a Lagrangian density function with high order derivatives of the field variables, is also discussed.

Lump and optical dromions for paraxial nonlinear Schrödinger equation

In this paper, we obtain lump soliton solutions for paraxial nonlinear Schrödinger equation (NLSE) with the aid of Hirota bilinear method (HBM). Lump soliton solutions are rational functions localized in all directions in the space. We also get optical dromions for paraxial NLSE by using the modified extended Tanh method. We get domain walls, singular dromions and combined dark-singular dromions. We also list the constraint conditions.

Exact Solutions for (2+1)-dimensional Nonlinear Schrödinger Equation Based on Modified Extended tanh Method

In this paper, modified extended tanh method is used to construct more general exact solutions of a (2+1)-dimensional nonlinear Schrödinger equation. With the aid of Maple and Matlab software, we obtain exact explicit kink wave solutions, peakon wave solutions, periodic wave solutions and so on and their images.

Modeling and analysis of fractional neutral disturbance waves in arterial vessels

The behavior of neutral disturbance in arterial vessels has attracted more and more attention in recent decades because it carries some important information which can be applied to predict and diagnose related heart disease, such as arteriosclerosis and hypertension, etc. Because of the complexity of blood flow in arteries, it is very necessary to construct accurate mathematical model and analyze the mechanical behavior of neutral disturbance in arterial vessels. In this paper, start from the basic equations of blood flow and the two-dimensional Navier–Stokes equation, the vorticity equation describing the disturbance flow is presented. Then, by use of multi-scale analysis and perturbation expansion method, the ZK equation is put forward which can reflect the behavior of the neutral perturbation flow in arterial vessels. Compared with the traditional KdV model, the model established in the paper can show the propagation of the disturbance flow in the radius direction. Furthermore, the time-fractional ZK equation is derived by semi-inverse method and Agrawal’s method, which is more convenient and accurate for discussing the feature of neutral disturbance in arterial vessels and can provide more information for analyzing some related heart disease. Meanwhile, with the help of the modified extended tanh method, the above mentioned equation is solved. The results show that neutral disturbance exists in arterial vessels and propagates in the form of solitary waves. By calculating, we find the relation of the stroke volume with vascular radius, blood flow velocity as well as the fractional order parameter α, which is very meaningful for preventing and treating related heart disease because the stroke volume is closely linked with heart disease.