A direct series method to find exact travelling wave solutions of nonlinear PDEs is appfied to Hirota's system of coupled Korteweg-de Vries equations and to the sine-Gordon equation. The straightforward but lengthy algebraic computations to obtain single and multi-soliton solutions can be carried ou
Integrals of nonlinear equations of evolution and solitary waves
β Scribed by Peter D. Lax
- Publisher
- John Wiley and Sons
- Year
- 1968
- Tongue
- English
- Weight
- 991 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0010-3640
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π SIMILAR VOLUMES
Consider herein are the stability of the solitary waves \(e^{-i \omega u s} e^{i \psi(x-t t)} a(x-v t)\) for the following nonlinear quintic derivative SchrΓΆdinger equation. \[ u_{t}=i u_{x x}+i\left(c_{3}|u|^{2}+c_{s}|u|^{4}\right) u+\left[\left(s_{0}+s_{2}|u|^{2}\right) u\right]_{v}, \quad u \in
Title ofprogram.' FORMINT Lie B'Γ‘cklund algebra or/and infinite series of nontrivial conservation laws. Some of these equations are interesting from the Catalogue number: ACDJ physical point of view due to their soliton solutions. Program obtainable from: CPC Program Library, Queen's Uni-Method of s
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