Bifurcation analysis on ion sound and Langmuir solitary waves solutions to the stochastic models with multiplicative noises.

This article explores on a stochastic couple models of ion sound as well as Langmuir surges propagation involving multiplicative noises. We concentrate on the analytical stochastic solutions including the travelling and solitary waves by using the planner dynamical systematic approach. To apply the method, First effort is to convert the system of equations into the ordinary differential form and present it in form of a dynamic structure. Next analyze the nature of the critical points of the system and obtain the phase portraits on various conditions of the corresponding parameters. The analytic solutions of the system in an account of distinct energy states for each phase orbit are performed. We also show how the results are highly effective and interesting to realize their exciting physical as well as the geometrical phenomena based on the demonstration of the stochastic system involving ion sound as well as Langmuir surges. Descriptions of effectiveness of the multiplicative noise on the obtained solutions of the model, and its corresponding figures are demonstrated numerically.

Development and validation of a simplified thoracolumbar spine fracture classification system.

STUDY DESIGN: Development and validation of fracture classification system. OBJECTIVE: To develop and validate a Simplified Classification System (SCS) for Thoraco-Lumbar (TL) fractures (SCS - TL fractures). SETTING: Tertiary Spinal Injuries Centre, New Delhi, India METHODS: Based on the International Spinal Cord Society Spine Trauma Study Group (ISCoS STSG, n = 23) experts' clinical consensus conducted by the senior author and on his own experience, the Denis classification for TL fractures was modified to develop a SCS-TL fractures that could guide the management. After Face and Content validation, Construct validation was done in two stages. First stage analyzed if management of 30 cases of TL fractures, as suggested by the SCS - TL fractures and ISCoS STSG (n = 9) as well as other (n = 5) experts, matched. Second stage was a one year prospective study analyzing if the management suggested matched the management actually carried out by different spine surgeons (n = 10) working at a single institution. RESULTS: In the first stage there was 100% agreement for management (conservative or surgical) as proposed by experts and that suggested by the proposed classification for TL fractures whereas for surgical approach there was 88% agreement. In the second stage, there was 100% agreement for the management as well as surgical approach as carried out at our centre and that proposed by the SCS for TL fractures. CONCLUSIONS: The proposed SCS-TL fractures helps in classifying and in decision making for management of TL fractures. The next phase of validation would involve multicentric reliability studies and prospective application of the SCS- TL fractures.

New extended (G'/G)-expansion method to solve nonlinear evolution equation: the (3 + 1)-dimensional potential-YTSF equation.

In this article, a new extended (G'/G) -expansion method has been proposed for constructing more general exact traveling wave solutions of nonlinear evolution equations with the aid of symbolic computation. In order to illustrate the validity and effectiveness of the method, we pick the (3 + 1)-dimensional potential-YTSF equation. As a result, abundant new and more general exact solutions have been achieved of this equation. It has been shown that the proposed method provides a powerful mathematical tool for solving nonlinear wave equations in applied mathematics, engineering and mathematical physics.