Exact solutions for isotropic random flights in odd dimensions

2012 ◽  
Vol 53 (10) ◽  
pp. 103504 ◽  
Author(s):  
Ricardo García-Pelayo
Keyword(s):  
Exact Solutions ◽  
Random Flights ◽  
Isotropic Random ◽  
Odd Dimensions

scholarly journals Higgs–Chern–Simons Gravity Models in d = 2n + 1 Dimensions

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2064
Author(s):  
Eugen Radu ◽  
D. H. Tchrakian
Keyword(s):  
Exact Solutions ◽  
Feature Vector ◽  
Scalar Fields ◽  
Gravity Models ◽  
One Step ◽  
Preliminary Study ◽  
Chern Simons ◽  
Odd Dimensions

We consider a family of new Higgs–Chern–Simons (HCS) gravity models in 2n+1 dimensions (n=1,2,3). This provides a generalization of the (usual) gravitational Chern–Simons (CS) gravities resulting from non-Abelian CS densities in all odd dimensions, which feature vector and scalar fields, in addition to the metric. The derivation of the new HCS gravitational (HCSG) actions follows the same method as in the usual-CSG case resulting from the usual CS densities. The HCSG result from the HCS densities, which result through a one-step descent of the Higgs–Chern–Pontryagin (HCP), with the latter being descended from Chern-Pontryagin (CP) densities in some even dimension. A preliminary study of the solutions of these models is considered, with exact solutions being reported for spacetime dimensions d=3,5.

Extended F-Expansion Method for Solving the modified Korteweg-de Vries (mKdV) Equation

2020 ◽  
Vol 11 (1) ◽  
pp. 93-100
Author(s):  
Vina Apriliani ◽  
Ikhsan Maulidi ◽  
Budi Azhari
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Internal Waves ◽  
Water Waves ◽  
Wave Equations ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Mkdv Equation ◽  
Innovative Methods ◽  
De Vries

One of the phenomenon in marine science that is often encountered is the phenomenon of water waves. Waves that occur below the surface of seawater are called internal waves. One of the mathematical models that can represent solitary internal waves is the modified Korteweg-de Vries (mKdV) equation. Many methods can be used to construct the solution of the mKdV wave equation, one of which is the extended F-expansion method. The purpose of this study is to determine the solution of the mKdV wave equation using the extended F-expansion method. The result of solving the mKdV wave equation is the exact solutions. The exact solutions of the mKdV wave equation are expressed in the Jacobi elliptic functions, trigonometric functions, and hyperbolic functions. From this research, it is expected to be able to add insight and knowledge about the implementation of the innovative methods for solving wave equations. 

Conserved Quantities for the General Linear Heat Equation

2016 ◽  
pp. 4437-4439
Author(s):  
Adil Jhangeer ◽  
Fahad Al-Mufadi
Keyword(s):  
Evolution Equation ◽  
Heat Equation ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Lagrangian Approach ◽  
General Linear ◽  
Conserved Quantities ◽  
Linear Heat ◽  
The Family ◽  
Partial Lagrangian

In this paper, conserved quantities are computed for a class of evolution equation by using the partial Noether approach [2]. The partial Lagrangian approach is applied to the considered equation, infinite many conservation laws are obtained depending on the coefficients of equation for each n. These results give potential systems for the family of considered equation, which are further helpful to compute the exact solutions.

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