𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Modified method of simplest equation: Powerful tool for obtaining exact and approximate traveling-wave solutions of nonlinear PDEs

✍ Scribed by Nikolay K. Vitanov

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
242 KB
Volume
16
Category
Article
ISSN
1007-5704

No coin nor oath required. For personal study only.

✦ Synopsis

We discuss the class of equations

where A ij (u), B kl (u) and C(u) are functions of u(x, t) as follows: (i) A ij , B kl and C are polynomials of u; or (ii) A ij , B kl and C can be reduced to polynomials of u by means of Taylor series for small values of u. For these two cases the above-mentioned class of equations consists of nonlinear PDEs with polynomial nonlinearities. We show that the modified method of simplest equation is powerful tool for obtaining exact traveling-wave solution of this class of equations. The balance equations for the sub-class of traveling-wave solutions of the investigated class of equations are obtained. We illustrate the method by obtaining exact traveling-wave solutions (i) of the Swift-Hohenberg equation and (ii) of the generalized Rayleigh equation for the cases when the extended tanh-equation or the equations of Bernoulli and Riccati are used as simplest equations.

πŸ“œ SIMILAR VOLUMES

On modified method of simplest equation
On modified method of simplest equation for obtaining exact and approximate solutions of nonlinear PDEs: The role of the simplest equation
✍ Nikolay K. Vitanov πŸ“‚ Article πŸ“… 2011 πŸ› Elsevier Science 🌐 English βš– 313 KB

of Bernoulli Equation of Riccati Elliptic equation a b s t r a c t The modified method of simplest equation is powerful tool for obtaining exact and approximate solutions of nonlinear PDEs. These solutions are constructed on the basis of solutions of more simple equations called simplest equations.

Application of the method of simplest eq
Application of the method of simplest equation for obtaining exact traveling-wave solutions for two classes of model PDEs from ecology and population dynamics
✍ Nikolay K. Vitanov; Zlatinka I. Dimitrova πŸ“‚ Article πŸ“… 2010 πŸ› Elsevier Science 🌐 English βš– 252 KB

of simplest equation Exact traveling-wave solutions a b s t r a c t We search for traveling-wave solutions of two classes of equations: (I.) Class of reaction-diffusion equations Above a, b, c are parameters and D and F depend on the population density Q. We obtain such solutions by the modified me

Application of simplest equations of Ber
Application of simplest equations of Bernoulli and Riccati kind for obtaining exact traveling-wave solutions for a class of PDEs with polynomial nonlinearity
✍ Nikolay K. Vitanov πŸ“‚ Article πŸ“… 2010 πŸ› Elsevier Science 🌐 English βš– 242 KB

We search for traveling-wave solutions of the class of equations where a p ; b q and l m are parameters. We obtain such solutions by the method of simplest equation for the cases when the simplest equation is the the equation of Bernoulli or the equation of Riccati. We modify the methodology of the

Modified Kudryashov method for finding e
Modified Kudryashov method for finding exact solitary wave solutions of higher-order nonlinear equations
✍ M. M. Kabir; A. Khajeh; E. Abdi Aghdam; A. Yousefi Koma πŸ“‚ Article πŸ“… 2010 πŸ› John Wiley and Sons 🌐 English βš– 332 KB πŸ‘ 1 views

In this paper, we use the modified Kudryashov method or the rational Exp-function method to construct the solitary traveling wave solutions of the Kuramoto-Sivashinsky (shortly KS) and seventh-order Sawada-Kotera (shortly sSK) equations. These equations play a very important role in the mathematical

On exact travelling wave solutions for t
On exact travelling wave solutions for two types of nonlinear equations and a generalized KP equation
✍ Shaoyong Lai; Y.H. Wu; B. Wiwatanapataphee πŸ“‚ Article πŸ“… 2008 πŸ› Elsevier Science 🌐 English βš– 154 KB

In this paper, we study two types of genuinely nonlinear K(n, n) equations and a generalized KP equation. By developing a mathematical method based on the reduction of order of nonlinear differential equations, we derive general formulas for the travelling wave solutions of the three equations. The