Computational Method for Finding of Soliton Solutions of a Nonlinear Shrödinger Equation

Author(s):  
Vyacheslav A. Trofimov ◽  
Svetlana A. Varentsova
Author(s):  
Lanre Akinyemi ◽  
Mehmet Şenol ◽  
Emad Az-Zo’bi ◽  
P. Veeresha ◽  
Udoh Akpan

In this paper, we examined four different forms of generalized (2+1)-dimensional Boussinesq–Kadomtsev–Petviashvili (B-KP)-like equations. In this connection, an accurate computational method based on the Riccati equation called sub-equation method and its Bäcklund transformation is employed. Using this method, numerous exact solutions that do not exist in the literature have been obtained in the form of trigonometric, hyperbolic, and rational. These solutions are of considerable importance in applied sciences, coastal, and ocean engineering, where the B–KP-like equations modeled for some significant physical phenomenon. The graph of the bright and dark solitons is presented in order to demonstrate the influence of different physical parameters on the solutions. All of the findings prove the stability, effectiveness, and accuracy of the proposed method.


2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Cesar A. Gómez S ◽  
Alvaro H. Salas ◽  
Bernardo Acevedo Frias

We study a new integrable KdV6 equation from the point of view of its exact solutions by using an improved computational method. A new approach to the projective Riccati equations method is implemented and used to construct traveling wave solutions for a new integrable system, which is equivalent to KdV6 equation. Periodic and soliton solutions are formally derived. Finally, some conclusions are given.


2018 ◽  
Vol 5 (1) ◽  
pp. 31-36
Author(s):  
Md Monirul Islam ◽  
Muztuba Ahbab ◽  
Md Robiul Islam ◽  
Md Humayun Kabir

For many solitary wave applications, various approximate models have been proposed. Certainly, the most famous solitary wave equations are the K-dV, BBM and Boussinesq equations. The K-dV equation was originally derived to describe shallow water waves in a rectangular channel. Surprisingly, the equation also models ion-acoustic waves and magneto-hydrodynamic waves in plasmas, waves in elastic rods, equatorial planetary waves, acoustic waves on a crystal lattice, and more. If we describe all of the above situation, we must be needed a solution function of their governing equations. The Tan-cot method is applied to obtain exact travelling wave solutions to the generalized Korteweg-de Vries (gK-dV) equation and generalized Benjamin-Bona- Mahony (BBM) equation which are important equations to evaluate wide variety of physical applications. In this paper we described the soliton behavior of gK-dV and BBM equations by analytical system especially using Tan-cot method and shown in graphically. GUB JOURNAL OF SCIENCE AND ENGINEERING, Vol 5(1), Dec 2018 P 31-36


2019 ◽  
Author(s):  
john andraos

This paper proposes a standardized format for the preparation of process green synthesis reports that can be applied to chemical syntheses of active pharmaceutical ingredients (APIs) of importance to the pharmaceutical industry. Such a report is comprised of the following eight sections: a synthesis scheme, a synthesis tree, radial pentagons and step E-factor breakdowns for each reaction step, a tabular summary of key material efficiency step and overall metrics for a synthesis plan, a mass process block diagram, an energy consumption audit based on heating and cooling reaction and auxiliary solvents, a summary of environmental and safety-hazard impacts based on organic solvent consumption using the Rowan solvent greenness index, and a cycle time process schedule. Illustrative examples of process green synthesis reports are given for the following pharmaceuticals: 5-HT2B and 5-HT7 receptors antagonist (Astellas Pharma), brivanib (Bristol-Myers Squibb), and orexin receptor agonist (Merck). Methods of ranking synthesis plans to a common target product are also discussed using 6 industrial synthesis plans of apixaban (Bristol-Myers Squibb) as a working example. The Borda count method is suggested as a facile and reliable computational method for ranking multiple synthesis plans to a common target product using the following 4 attributes obtained from a process green synthesis report: process mass intensity, mass of sacrificial reagents used per kg of product, input enthalpic energy for solvents, and Rowan solvent greenness index for organic solvents.<br>


2018 ◽  
Vol 69 (10) ◽  
pp. 2633-2637
Author(s):  
Raluca Dragomir ◽  
Paul Rosca ◽  
Cristina Popa

The main objectives of the present paper are to adaptation the five-kinetic model of the catalytic cracking process and simulation the riser to predicts the FCC products yields when one of the major input variable of the process is change. The simulation and adaptation are based on the industrial data from Romanian refinery. The adaptation is realize using a computational method from Optimization Toolbox from Matlab programming language. The new model can be used for optimization and control of FCC riser.


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