𝔖 Bobbio Scriptorium
✦   LIBER   ✦

New exact travelling wave solutions to the complex coupled KdV equations and modified KdV equation

✍ Scribed by Huiqun Zhang

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
122 KB
Volume
13
Category
Article
ISSN
1007-5704

No coin nor oath required. For personal study only.

✦ Synopsis

By using some exact solutions of an auxiliary ordinary differential equation, a new direct algebraic method is described to construct the exact complex solutions for nonlinear partial differential equations. The method is implemented for the complex coupled KdV equations and modified KdV equation. New exact complex solutions are obtained.

πŸ“œ SIMILAR VOLUMES

On traveling wave solutions to combined
On traveling wave solutions to combined KdV–mKdV equation and modified Burgers–KdV equation
✍ Ahmet Bekir πŸ“‚ Article πŸ“… 2009 πŸ› Elsevier Science 🌐 English βš– 160 KB

In this work, we established exact solutions for some nonlinear evolution equations. The extended tanh method was used to construct solitary and soliton solutions of nonlinear evolution equations. The extended tanh method presents a wider applicability for handling nonlinear wave equations.

Exact solutions to the combined KdV and
Exact solutions to the combined KdV and mKdV equation
✍ M. N. B. Mohamad πŸ“‚ Article πŸ“… 1992 πŸ› John Wiley and Sons 🌐 English βš– 258 KB

## Abstract This paper presents two different methods for the construction of exact solutions to the combined KdV and mKdV equation. The first method is a direct one based on a general form of solution to both the KdV and the modified KdV (mKdV) equations. The second method is a leading order analy

New sets of solitary wave solutions to t
New sets of solitary wave solutions to the KdV, mKdV, and the generalized KdV equations
✍ Abdul-Majid Wazwaz πŸ“‚ Article πŸ“… 2008 πŸ› Elsevier Science 🌐 English βš– 145 KB

In this work we introduce new schemes, each combines two hyperbolic functions, to study the KdV, mKdV, and the generalized KdV equations. It is shown that this class of equations gives conventional solitons and periodic solutions. We also show that the proposed schemes develop sets of entirely new s

Solitary wave solutions and cnoidal wave
Solitary wave solutions and cnoidal wave solutions to the combined KdV and mKdV equation
✍ Sen-Yue Lou; Li-Li Chen πŸ“‚ Article πŸ“… 1994 πŸ› John Wiley and Sons 🌐 English βš– 370 KB

## Abstract This paper presents a mapping approach for the construction of exact solutions to the combined KdV and mKdV equation. There exist two types of soliton solutions which will reduce back to those of the KdV and mKdV equations in some appropriate limits. Four types of the general cnoidal wa