We present particular solutions for the following important nonlinear second order differential equations: modified Emden, generalized Lienard, convective Fisher, and generalized Burgers-Huxley. For the latter two equations these solutions are obtained in the travelling frame. All these particular solutions are the result of extending a simple and efficient factorization method that we develope...

restudied Huxley's measurements of Uca pugnax and presented not only a two-parameter power function but also a three-parameter power function; this three-parameter model 'is better than the two-parameter model for describing the observations'. The two-parameter model has a biological meaning, as explained by Huxley (Huxley, 1924); the three-parameter model has no biological meaning. I have show...

Class Meeting # 24: Transport Equations and Burger’s Equation In these notes, we introduce a class of evolution PDEs known as transport equations. Such equations arise in a physical context whenever a quantity is “transported” in a certain direction. Some important physical examples include the mass density flow for an incompressible fluid, and the Boltzmann equation of kinetic theory. We discu...

Ion-acoustic solitary and shock waves in dense quantum plasmas whose constituents are electrons, positrons, and positive ions are investigated. We assume that ion velocity is weakly relativistic and also the effects of kinematic viscosity among the plasma constituents is considered. By using the reductive perturbation method, the Korteweg–deVries–Burger (KdV-B) equation is derived. Keywords—Ion...

Abstract: A new periodic wave solution in terms of Riemann theta functions to the elliptic equation is presented, then by using this solution and the improved generalized F-expansion method, some exact solutions in terms of Riemann theta functions to the KdV-Burgers-Kuramoto(KBK) equation are obtained with the aid of Mathematica, their properties and profiles are displayed in their figures. To ...

This article deals with the solution of Cauchy problem for Inviscid Burger equation. Various numerical techniques like Upwind non Conservative, Lax Friedrich, Wendorff, and Mac Cormack, are used to solve initial-value problems Through various model problems, efficiency accuracy have been shown via graphical tabulated form exact solution.