Optical soliton perturbation with Kudryashov’s law of refractive index by modified sub-ODE approach

This paper implements the sub-ODE method and a wide spectrum of solitons are recovered for Kudryashov’s law of refractive index. The self-phase modulation comprises of four nonlinear components of refractive index. The perturbation terms are all of Hamiltonian type and are considered with maximum intensity. The solutions are written in terms of Weierstrass’ elliptic functions and Jacobi’s elliptic function. With the modulus of ellipticity approaching zero or unity, soliton solutions emerge.

New optical soliton solutions of Biswas–Arshed model with Kerr law nonlinearity

In this paper, the newly derived solutions for the optical soliton of Kerr law nonlinearity form of Biswas–Arshed model are investigated. The exact solutions are extracted by deploying two different novel methods namely, [Formula: see text]-expansion method and Riccati–Bernoulli sub-ODE method. Furthermore, in different conditions, the resultants show different wave solutions like singular, kink, anti-kink, periodic, rational, exponential and dark soliton solutions. Also, the dynamics of the attained solutions are presented graphically.

Exact propagation of the isolated waves model described by the three coupled nonlinear Maccari’s system with complex structure

In this paper, the three nonlinear Maccari’s-system (TNLMS) which describes how isolated waves are propagated in a finite region of space is studied. New accurate wave solutions of this model are obtained for the first time using the Riccati–Bernoulli Sub-ODE method (RBSOM) that treats the problem for which the balance rule fails. The efficiency of this method for constructing these exact solutions has been demonstrated. The obtained results give an accurate interpretation of the propagation of these isolated waves. With an appropriate values for the physical parameters, some representative wave structures are graphically presented.

Exact solutions of Hirota–Maccari system forced by multiplicative noise in the Itô sense

In this article, the stochastic Hirota–Maccari system forced in the Itô sense by multiplicative noise is considered. We just use the He’s semi-inverse method, sine–cosine method, and Riccati–Bernoulli sub-ODE method to get new stochastic solutions which are hyperbolic, trigonometric, and rational. The major benefit of these three approaches is that they can be used to solve similar models. Furthermore, we plot 3D surfaces of analytical solutions obtained in this article by using MATLAB to illustrate the effect of multiplicative noise on the exact solution of the Hirota–Maccari method.

An Introduction to Development of Centralized and Distributed Stochastic Approximation Algorithm with Expanding Truncations

The stochastic approximation algorithm (SAA), starting from the pioneer work by Robbins and Monro in 1950s, has been successfully applied in systems and control, statistics, machine learning, and so forth. In this paper, we will review the development of SAA in China, to be specific, the stochastic approximation algorithm with expanding truncations (SAAWET) developed by Han-Fu Chen and his colleagues during the past 35 years. We first review the historical development for the centralized algorithm including the probabilistic method (PM) and the ordinary differential equation (ODE) method for SAA and the trajectory-subsequence method for SAAWET. Then, we will give an application example of SAAWET to the recursive principal component analysis. We will also introduce the recent progress on SAAWET in a networked and distributed setting, named the distributed SAAWET (DSAAWET).

New shape of the chirped bright, dark optical solitons and complex solutions for (2+1) Ginzburg-Landau equation

Investigation of the Ginzburg-Landau equation (GLE) was done to secure new chirped bright, dark periodic and singular function solutions. For this, we used the traveling wave hypothesis and the chirp component. From there it was pointed out the constraint relation to the dierent arbitrary parameters of the GLE. Thereafter, we employed the improved sub-ODE method to handle the nonlinear ordinary differential equation (NODE). It was highlighted the virtue of the used analytical method via new chirped solitary waves. In our knowledge, these results are new, and will be helpful to explain physical phenomenons.

New Lump Solutions for Spatio-Temporal Dispersion (1+1)-Dimensional Ito-Equation

From point of view of two different schemas several new impressive lump solutions to (1+1)-dimensional Ito equation have been established. The first schema is the Paul-Painleve approach method (PPAM) which will be applied perfectly to extract multiple lump solutions of this model, while the second schema is the famous one of the ansatze method and has personal profile named the Ricatti-Bernolli Sub-ODE method. In related subject the numerical solutions corresponding to all lump solutions achieved via each method have been demonstrated individually in the framework of the variational iteration method (VIM).

DISPERSIVE SOLITARY WAVE SOLUTIONS OF COUPLING BOITI-LEON-PEMPINELLI SYSTEM USING TWO DIFFERENT METHODS

In this paper, new exact traveling wave solutions for the coupling Boiti-Leon-Pempinelli system are obtained by using two important different methods. The first is the modified extended tanh function methods which depend on the balance rule and the second is the Ricatti-Bernoulli Sub-ODE method which doesn’t depend on the balance rule. The solitary waves solutions can be derived from the exact wave solutions by give the parameters a special value. The consistent and inconsistent of the obtained solutions are studied not only between these two methods but also with that relisted by the other methods.